Some Fr\'echet algebras for which the Chern character is an isomorphism
  Using similarities between topological $K$-theory and periodic cyclic homology we show that, after tensoring with $\mathbb C$, for certain Fr\'echet algebras the Chern character provides an isomorphism between these functors. This is applied to prove that the Hecke algebra and the Schwartz algebra of a reductive $p$-adic group have isomorphic periodic cyclic homology.   The main theorem in the first version was incorrect for algebras related to noncompact manifolds. This has no effect on the results concerning p-adic groups.   In the appendix we show that an analogous cohomological result does hold in the noncompact case. 
Maarten Solleveld