### Local Cyclic Cohomology of Group Banach Algebras and the bivariant Chern-Connes Character of the Gamma-Element, by Michael Puschnigg

We compute the local cyclic cohomology of the group Banach algebra of
fundamental groups of compact manifolds of nonpositive curvature.

This is essentially the first calculation of local cyclic cohomology by
means of resolutions and the explicit definition of the local cyclic
complex. We use this calculation to determine the image of Kasparov's gamma
element under the bivariant Chern-Connes character in bivariant local cyclic
cohomology for groups satisfying in addition the property of rapid decay.

Michael Puschnigg <puschni@math.uni-muenster.de>