3 problems

Let $G$ be a topological group with a universal proper space $\mathcal E G$. Let $A$ be a $C^*$-algebra and let $B$ be a $G$-algebra. Define the naive topological $KK$-groups by ……

Functoriality conjecture. The class $\Omega_!(g\circ f)$ should be identified, up to a canonical bordism, with

Spectrum conjecture. For every finite group $G$, the natural map