  Let H be a graded Hecke algebra with complex deformation parameters and Weyl
group W. We show that the Hochschild, cyclic and periodic cyclic homologies of
H are all independent of the parameters, and compute them explicitly. We use
this to prove that, if the deformation parameters are real, the collection of
irreducible tempered H-modules with real central character forms a Q-basis of
the representation ring of W.
  Our method involves a new interpretation of the periodic cyclic homology of
finite type algebras, in terms of the cohomology of a sheaf over the underlying
complex affine variety.
