Crossed products of C*-algebras by endomorphisms

The concept of a twisted crossed product associated to a non-classical C^*-dynamical system is introduced and studied. The relationship between a covariant projective representation of the system and the corresponding induced representation of the twisted crossed product is investigated, particularly from the point of view of determining when the induced representation is faithful. Conditions are given on the C^*-dynamical system that ensure nuclearity, simplicity or primeness of the twisted crossed product.