  A refined form of the `Folk Theorem' that a smooth action by a compact Lie
group can be (canonically) resolved, by iterated blow up, to have unique
isotropy type was established by the authors in the context of manifolds with
corners; the canonical construction induces fibrations on the boundary faces of
the resolution resulting in an `equivariant resolution structure'. Here,
equivariant K-theory and the Cartan model for equivariant cohomology are
tracked under the resolution procedure as is the delocalized equivariant
cohomology of Baum, Brylinski and MacPherson. This leads to resolved models for
each of these cohomology theories, in terms of relative objects over the
resolution structure and hence to reduced models as flat-twisted relative
objects over the resolution of the quotient. An explicit equivariant Chern
character is then constructed, essentially as in the non-equivariant case, over
the resolution of the quotient.
