Paper detail

Deformation of operator algebras by Borel cocycles

Assume that we are given a coaction δof a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle ωon G. Motivated by the approach of Kasprzak to Rieffel's deformation we define a deformation A_ωof A. Among other properties of A_ωwe show that A_ω\otimes K(L^2(G)) is canonically isomorphic to A\rtimes_δ\hat G\rtimes_{\hatδ,ω}G. This, together with a slight extension of a result of Echterhoff et al., implies that for groups satisfying the Baum-Connes conjecture the K-theory of A_ωremains invariant under homotopies of omega.