Endomorphism Algebras of Equivariant Exceptional Collections

Abstract Given an action of a finite group on a triangulated category with a suitable strong exceptional collection, a construction of Elagin produces an associated strong exceptional collection on the equivariant category. In the untwisted case, we prove that the endomorphism algebra of the induced exceptional collection is the basic reduction of the skew group algebra of the endomorphism algebra of the original exceptional collection.