Equivariant KK-theory and model categories

KK-theory can be seen as a homotopy theory for C*-algebras. It is plausible to ask whether it can be cast in the framework of abstract homotopy theory. In the non-equivariant case, Joachim-Johnson showed in 2007 that KK-groups can in fact are the homotopy groups of a stable model structure on pro-C*-algebras. I will discuss similar results in the equivariant case, with a locally compact group action on the algebras involved. Some new techniques involving universal equivariant algebras were needed in the construction which would also be discussed. Lastly, a comparison would be made to the more recent infinity categorical equivariant KK-theory a'la Bunke-Engel-Land.