The band's name is "The Shins" but the music in that ad was written by James Mercer. I think they'd taken the ad out of the gap website. You used to be able to view it there.
If you go to www.theshins.com you can listen to song samples for free. You may also visit www.subpop.com if you want to see quicktime videos and stuff. I happen to love this band alot. If you watched Garden State, some of their songs were featured in the movie.