Equivariant higher-index problems for proper actions and nonpositively curved manifolds (Q778847)

The paper under review proves the injectivity of an equivariant higher index map which generalizes both the (classical) Baum-Connes map and the ``coarse'' Baum-Connes map introduced by John Roe. Namely, this map is \[\mu^{\Gamma} : \lim_{d \to \infty} K^{\Gamma}_*(P_d(X)) \to K_*(C^*(X)^{\Gamma})\] where \(\Gamma\) is a countable discrete group which acts proerly and isometrically on the metric space \(X\). The assumptions that lead to this result are that \(X\) is discrete with bounded geometry and admits a coarse embedding to a simply connected, complete Riemannian manifold \(M\) with nonpositive sectional curvature.