There were years when a bunch of French Canadians played for the French ice hockey team in the Olympics. (And the one year that Great Britain actually won the hockey gold medal -- seriously, look it up -- the team in reality consisted of all Canadians.)
Last Winter Olympics, a Jewish American pairs figure skaters who never spent a day in Israel, represented Israel in the Olympics. This happens often with Jews around the world because of Israel's "birthright" citizenship laws.
The last Summer Olympics, there was a huge controversy over an American woman basketball player, with absolutely no ties to Russia (except like one grandparent who had some sort of Russian ancestry) who was playing professionally in a Russian club league, got cut from the American national team, and then Russia offered her "citizenship" if she wanted to play for Russia. She took the offer. She got lambasted by other American players who knew her from their college playing days.
