This world premiere musical springs from Green Day’s multiplatinum album, which sold more than 12 million copies worldwide and won two Grammys. The show apparently involves the search for redemption by a group of working-class characters, moving from the suburbs to the city, with one going as far as the Middle East. Directed by Michael Mayer, who won a Tony for his magnificent staging of the seamless rock musical “Spring Awakening,†the production contains every track from the album as well songs from Green Day’s new release, “21st Century Breakdown.†Berkeley Rep’s website warns fans that Green Day will not be performing but has nonetheless instituted a policy in which “no more than 10 tickets may be purchased per household.†Ha! Just try to keep the band’s army of groupies at bay.