A new approach to deformation of $C^*$-algebras via coactions

We revisit the procedure of deformation of $C^*$-algebras via coactions of locally compact groups and extend the methods to cover deformations for maximal, reduced, and exotic coactions for a given group $G$ and circle-valued Borel $2$-cocycles on $G$. In the special case of reduced (or normal) coactions our deformation method substantially differs from – but turns out to be equivalent to – the ones used by previous authors, specially those given by Bhowmick, Neshveyev, and Sangha (2013).

Our approach yields all expected results, like a good behaviour of deformations under nuclearity, continuity of fields of $C^*$-algebras and $K$-theory invariance under mild conditions.