Homological invariants of group Banach algebras of discrete groups

Several conjectures about « assembly maps » in $K$-theory (Baum-Connes Conjecture) and surgery theory (Borel Conjecture) rank among the most significant open problems about discrete groups.

In this talk we will present some recent progress on a similar conjecture about the assembly map in local cyclic homology for discrete, cocompact isometry groups of $CAT(0)$-spaces.