Decomposition theorems for certain C*-crossed products

Abstract

Let G be an abelian discrete group, A a unital C*-algebra and an action of G on A, i.e. (A, G,) is a C*-dynamical system. Let K denote the kernel ker of and put R = G/K. The main purpose of this article is to determine the roles of K and R in the crossed product G A. This goal is achieved in Section 2, where we prove that G A is *-isomorphic to a twisted crossed product of R with C*(K) A with respect to the action 1 and a 2-cocycle related to the 2-cocycle determined by the extension G of R by K. Here is the obvious action of R on A.