Deformation of algebras associated with group cocycles

Abstract

We study deformation of algebras with coaction symmetry of reduced algebras of discrete groups, where the deformation parameter is givenby a continuous family of group $2$-cocycles. When the group satisfies the Baum–Connes conjecture with coefficients, we obtain an isomorphism of K-groups of the deformed algebras. This extends both the $\theta$-deformation of Rieffel on ${\mathbb{T}}^n$-actions, and a recent result of Echterhoff, Lück, Phillips, and Walters on the K-groups on the twisted group algebras.