Triano coached the team from 1998 to 2004, when his firing prompted harsh words from Nash and bad feelings in much of the Canadian basketball community. It is not considered a coincidence that Nash has not suited up for Canada since.  Triano continued to work as an N.B.A. assistant before taking over as the head coach of the Toronto Raptors last year. He could not be more tickled with his new assignment with the United States team.  “It’s a great honor,” Triano said. “These are the best basketball players in the world and some of the best coaches in the world. It’s a great opportunity for me to be able to learn from them and help out in any way I can.”  For much of his life, Triano has been crossing the border to chase the standard of American basketball, a game invented by another Canadian, James Naismith.  Brian Mulligan, one of his youth coaches in Niagara Falls, Ontario, recalls taking teams over the border to play American teams when Triano was 10 and playing for St. Patrick’s church.  Triano rooted for the old Buffalo Braves of the N.B.A., and he watched Frank Layden’s and Calvin Murphy’s great teams at Niagara University with awe.  Triano’s high school travel teams would head to Buffalo for games. In college at Simon Fraser in British Columbia, Triano drove over the border on weekends to play for an A.A.U. team in Washington known as the Brewster Applepackers. (Lorenzo Romar, now the University of Washington coach, was a teammate.)  “The basketball people really follow the American teams here,” said Mulligan, 65, who is now an assistant at Brock University in St. Catharines, Ontario. “If you can ever beat an American team, you would know you’ve done well.”  Before joining the Americans, Triano had one of his fondest accomplishments: beating them. At the World University Games in Edmonton, Alberta, in 1983, Triano led the Canadians to a semifinal upset of an American team with Charles Barkley and Karl Malone. In the final, Canada beat Yugoslavia, led by Drazen Petrovic. Triano considers that run the highlight of his national team experience, along with being named coach.  “One of the greatest things I always felt was to come back and coach in the Olympics, to give 12 more guys the same opportunity that I had,” he said. “That’s what really made me want to be a coach.”  Triano’s firing from the team was ugly, and the move was panned in the Canadian news media. Triano stayed quiet, however, and became further invested in being an N.B.A. coach.  His N.B.A. experience, combined with his international playing and coaching experience, made Triano well suited to replace the internationally savvy D’Antoni.  Triano said he did feel strange putting on the USA logo. He had served as a coach for USA Basketball select teams, which scrimmage the national team during the summers. He said he had coached Derrick Rose, Kevin Durant and Andre Iguodala, three of the United States’ current starters, on those teams.  Mulligan said the reaction in Canada to Triano’s more formal coaching role had been gleeful.  “I think that it’s one of the best things that has happened to basketball in Canada,” Mulligan said. “It legitimizes the programs we do here.”  Triano is unassuming and played down his role on the staff, which he said included splitting scouting duties with his fellow assistant Nate McMillan. But from Colangelo to Coach Mike Krzyzewski, there is little doubting Triano’s value.  “That experience of understanding the international game is invaluable,” Krzyzewski said. “For someone like Jay to fill in, there is no one like Jay. We’re very fortunate to have that.”  Perhaps the most obvious signal shown by luring Triano is that the Americans, trying to break out of an international slump, have their priorities straight.  “I think it says that we want to win,” center Tyson Chandler said of Triano’s presence. “It doesn’t matter who can help us get there. We want to win.”  A version of this article appears in print on August 28, 2010, on Page D2 of the New York edition with the headline: Canada With the Assist. Order Reprints| Today's Paper|Subscribe
Jay Triano, who played 11 years for Canada and was its coach from 1998 to 2004, has replaced the assistant coach Mike D’Antoni, who had back problems.