From MangaHelpers:

This manga is related to the "Date A Live" novel and anime. It features members of the AST (AntiSpirit Team), a special squad devoted to fighting spirits. Okamine Mikie idolizes her superior AST member, Tobiichi Origami, and may be in love with her as well. Unfortunately, Origami seems to want nothing to do with her. One day, they end up heading toward an explosion that wasn't caused by a spirit. Instead, it was caused by a girl named Ashley Sinclair, who transfers to their school shortly after the incident! [tethysdust]