Twisted equivariant $K$–theory and $K$–homology of $\mathrm{Sl}_3{\mathbb{Z}}$

Abstract

We use a spectral sequence to compute twisted equivariant $K$–theory groups for the classifying space of proper actions of discrete groups. We study a form of Poincaré duality for twisted equivariant $K$–theory studied by Echterhoff, Emerson and Kim in the context of the Baum–Connes conjecture with coefficients and verify it for the group ${Sl}_3\left(\mathbb{Z}\right)$.