  In a strengthening of the G-Signature Theorem of Atiyah and Singer, we
compute, at least in principle (modulo certain torsion of exponent dividing a
power of the order of G), the class in equivariant K-homology of the signature
operator on a G-manifold, localized at a prime idea of R(G), in terms of the
classes in non-equivariant K-homology of the signature operators on fixed sets.
The main innovations are that the calculation takes (at least some) torsion
into account, and that we are able to extend the calculation to some non-smooth
actions.
