  We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We
then show that the Hochschild cohomology ring modulo nilpotence is a finitely
generated algebra of Krull dimension 2, and describe the support varieties of
modules for these algebras. As a consequence we obtain the result that the
Hochschild cohomology ring modulo nilpotence of a Hecke algebra has Krull
dimension 1 if the algebra is of finite type and has Krull dimension 2 if the
algebra is of tame type.
