The coarse Baum-Connes conjecture via C0 coarse geometry

The C0 coarse structure on a metric space is a refinement of the bounded structure and is closely related to the topology of the space. In this paper we will prove the C0 version of the coarse Baum-Connes conjecture and show that K*(C*X0) is a topological invariant for a broad class of metric spaces. Using this result we construct a 'geometric' obstruction group to the coarse Baum-Connes conjecture for the bounded coarse structure. We then show under the assumption of finite asymptotic dimension that the obstructions vanish, and hence we obtain a new proof of the coarse Baum-Connes conjecture in this context.