Deformation of algebras associated with group cocycles

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.