### The G-Signature Theorem revisited, by Jonathan Rosenberg

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.

Jonathan Rosenberg <jmr@math.umd.edu>