On March 3, 2012, two of the group members, Nadezhda Tolokonnikova and Maria Alyokhina, were arrested and charged with hooliganism. A third member, Yekaterina Samutsevich, was arrested on March 16. Denied bail, they were held in custody until their trial began in late July. On August 17, 2012, the three members were convicted of “hooliganism motivated by religious hatred”, and each was sentenced to two years imprisonment.
http://rt.com/news/pussy-riot-trial-896/
http://www.bbc.co.uk/news/world-europe-19297373
http://www.theguardian.com/music/2012/aug/17/pussy-riot-sentenced-prison-putin?newsfeed=true
AFAIK, in the US the only crime they could have been charged with is trespassing.