Group quasi-representations and almost flat bundles (Q2450778)

Summary: We study the existence of quasi-representations of discrete groups \(G\) into unitary groups \(U(n)\) that induce prescribed partial maps \(K_0(C^*(G))\to \mathbb{Z}\) on the \(K\)-theory of the group \(C^*\)-algebra of \(G\). We give conditions for a discrete group \(G\) under which the \(K\)-theory group of the classifying space \(BG\) consists entirely of almost flat classes.