Deformation of algebras associated with group cocycles

Abstract: We study deformation of algebras with coaction symmetry of reduced algebra of discrete groups, where the deformation parameter is given continuous family of group $2$-cocycles. When the group satisfies the Baum-Connes conjecture with coefficients, we obtain 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, L\"{u}ck, Phillips, and Walters on the K-groups on the twisted group algebras.