By JAMES MONTAGUEDEC. 15, 2014

PEJA, Kosovo — Up a steep hill on a narrow, unlit road in this town near the Montenegrin border, the Toni Kuka Judo School was filled with the smell of sweat, smoke and winter.

Inside, 26 judokas dressed in blue or white uniforms arranged themselves in pairs around the blue-and-yellow tatami mat. The flags of Kosovo and Japan hung above a mirrored wall clouded in condensation. An old wood stove smoked heavily; it was fed fuel periodically by a young girl to keep the biting December cold at bay. When the fuel stopped, the mirrors cleared as the cold encroached like an unwelcome guest.

The 26 boys and girls bowed and gripped their opponents. “Hajime!” shouted Driton Kuka, the 42-year-old coach of Kosovo’s national judo squad.

Begin.

It was just another day of training in the school, but Kosovar athletes soon welcomed a new day altogether. Twenty-four hours later, the International Olympic Committee voted to admit Kosovo as a full member, granting the province’s athletes the right to compete as an independent team in international competitions.

Without that recognition, which had been provisionally approved in October, Kosovo’s athletes had been barred from competing under the country’s flag at elite competitions like the Olympics. A few, like the two-time judo world champion Majlinda Kelmendi, had broken through anyway. Kelmendi, 23, made it to the London Olympics in 2012 by competing for Albania, and she could be a medal favorite in Rio de Janeiro in 2016.

But even as a world champion in the 52-kilogram weight division (about 115 pounds), she said, she often feels like an outsider.

“More than any other athlete, I have that feeling of being ignored or not the same as other athletes in the world,” Kelmendi said.

Discussing her brief appearance in London, she added: “I was not allowed to have my flag or my anthem. I’m happy it will not happen again. We will be the same as every athlete in the world.”

Despite being recognized by 23 of the 28 European Union states and 108 United Nations members, Kosovo remains unrecognized as a fully independent state. The quest for recognition, however, has gone far beyond politics.

Kosovo’s national sports associations have fought a largely losing battle in the face of strong opposition from Serbian and Russian officials. Serbia maintains that Kosovo is an inviolable part of its sovereign territory, as does its ally Russia, which can veto any substantive resolution of the United Nations Security Council. On a recent visit to Belgrade, President Vladimir V. Putin of Russia reiterated that his country would never recognize Kosovo.

Kosovo does not have recognition from many major international federations represented at the Olympics, including those for basketball, swimming, and track and field. The International Judo Federation is one of the few to have officially recognized Kosovo, in 2012. When Kelmendi won her first world title, in 2013, she represented Kosovo. But politics have encroached on her career. At the 2014 world championships in Chelyabinsk, Russia, she was told that she would compete under the judo federation’s flag.
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“It was a big surprise for us,” Kelmendi said. “I went there to represent my country, and I was not allowed.”

Putin is an eighth dan judoka, an honorary member of the federation and a co-author of a Russian book on judo. He attended the final day of competition.

“It makes me angry inside, not scared,” Kelmendi said of her international isolation. “I wanted to prove that even if I’m not representing my country, I’m the best in the world.” She easily retained her title in the final.

Her coach, Kuka, was once a promising judoka, a champion in the former Yugoslavia destined to challenge for a medal at the 1992 Barcelona Olympics. But the rising tensions that led to Yugoslavia’s civil war, Kuka said, meant that the country’s Kosovar athletes boycotted all international competitions. Kuka said the decision was made “to let the international community know that we are living like the people of the second hand, as they say.”

His two houses were destroyed during the 1998-99 Kosovo War, but his half-built judo school survived.

“Our dojo was a bit lucky,” he said. “It was not finished. It was just the walls. They couldn’t burn it down.”

Although he never had the chance to compete for an Olympic medal, Kuka said that coaching Kelmendi had given him the chance to relive the dream he sacrificed.

“When I look at Majlinda in competition, I see myself, to continue what I stopped because of politics and the war,” he said. “If we will get an Olympic medal, and the next day my life will be finished, this is O.K. It is my goal in life.”

Other unrecognized sports, like swimming, have not fared as well. From Kosovo’s capital, Pristina, the nearest Olympic pool is a five-hour drive. Rita Zeqiri, who has won six national championships, regularly made the trip and practiced in hotel pools. Later she trained in a one-lane, 25-meter pool built by her father in her backyard. (He then sank the rest of his savings into the construction of the larger indoor pool that Zeqiri, a law student, trains in today.)

“I was going to give up swimming,” Zeqiri said between sessions last week. “The drive to Macedonia was five hours, and I couldn’t go to school. But my father just finished the pool. So I started to swim again. But I need a 50-meter pool.”

The Kosovo men’s champion Lum Zhaveli, 24, works as a computer programmer. He lost a year of training after contracting pneumonia from regularly breathing the air at a badly maintained pool in Pristina. “Nothing can surpass the Olympics,” he said. “But now I can’t go to all the competitions. It is difficult to get visas being Kosovar.”

The I.O.C.'s vote on Tuesday to grant Kosovo full membership provoked a strong reaction in Belgrade. Serbia’s minister for sport, the former Olympian Vanja Udovicic, said in a statement that the decision “gives room for future precedents that could jeopardize world sports.”

In Pristina, Kosovo’s deputy foreign minister, Petrit Selemi, hailed the decision.

“Kosovars are celebrating probably the most important day since the declaration of independence” in 2008, he said, adding: “Modern nations aren’t just about the E.U., Council of Europe and the U.N. They are also about forging modern identities, and having an Olympic team is as much a marker of national identity and pride.”

The logistics and politics of preparing Kosovo’s athletes for Rio 2016 remain difficult to negotiate. It is still unclear whether athletes will be allowed to compete in sports if their individual federations have not recognized Kosovo.

“Discussions with the relevant international federations will take place on a case-by-case basis,” the I.O.C. said. When asked what would happen if a sport’s federation refused to recognize Kosovo, an I.O.C. spokeswoman said in an email that the organization would not “speculate on hypothetical scenarios.”

Kosovo’s athletes are not waiting. On the afternoon of the vote, the first snow of the winter fell on Pristina’s huge Hall of Sports. Behind every door in its concrete labyrinth of basement corridors, athletes were training for an Olympic dream. Behind one door, on top of ripped floor mats, the 19-year-old wrestler Dardan Syla trained with his father, a former wrestler who once represented Yugoslavia.

In other rooms, table tennis players, gymnasts and boxers threw themselves into their preparations.

“I’m training as much as I can,” Fatom Tolaj, 20, said after he finished sparring with the Pristina Boxing Club. “I hope I will go to Rio. It would be a dream. Why not? For every sportsman, it is a dream to go to the Olympiad.”

Kosovo’s best medal hopes still rest on the one athlete who will almost certainly be in Rio. Kelmendi’s world title means she is virtually guaranteed a place, and now that Kosovo has been recognized, I.O.C. rules allow her to switch her nationality.

“My main goal now is the Olympic Games, because at the moment I am the best in the world,” she said after training had finished and the wooden stove had been left to burn out. “I know it’s hard. But it is not impossible. I don’t do anything else. I eat. I sleep. I train. That is it.”