The Bass conjecture and group von Neumann algebras (Q1568677)

Let \(G\) be a discrete group. Let \(\mathbb{Z} G\) be its integral group ring. The group von Neumann algebra \({\mathcal N}(G)\) is the weak closure of the complex group ring \(\mathbb{C} G\) considered as subring of the \(C^*\)-algebra of bounded operators \({\mathcal B}(l^2(G))\) from \(l^2(G)\) to itself. The inclusion \(\mathbb{Z} G\) to \({\mathcal N}(G)\) induces a homomorphism \(\widetilde K_0(\mathbb{Z} G)\to \widetilde K_0({\mathcal N}(G))\). The main result of the paper says that this homomorphism is trivial.