Baum-Connes conjecture states that for a locally compact group $G$ the so called assebly map $\mu$ between $G$-equivariant K-homology of the universal example for proper actions of $G$ and K-theory of $C^*_r(G)$ (the reduced $C^*$-algebra of the group) is an isomorphism. Is there an example of the group $G$ such that:
- It is not known whether Baum-Connes conjecture for this group holds but
- Groups $K_G(\underline{E}G)$ and $K(C^*_r(G))$ are abstracly isomorphic and nontrivial.