The Baum–Connes conjecture via localisation of categories

We redefine the Baum–Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the Baum–Connes assembly map for other equivariant homology theories. We extend many of the known techniques for proving the Baum–Connes conjecture to this more general setting.