Equivariant bivariant K-theory for bornological algebras

We introduce equivariant bivariant K-theory for bornological algebras by taking a presentable refinement of the bivariant K-theory of Lafforgue and Paravicini. An upshot of this refinement is that we may purely formally define a Bost-Connes assembly map via localisation in the sense of Meyer-Nest. Another feature built into the refinement is a large UCT-class; on this UCT-class, we show that the rationalised Chern-Connes character from KK-theory to local cyclic homology is an equivalence. This is joint work with Anupam Datta.