  Let H(G) be the Hecke algebra of a reductive p-adic group G. We formulate a
conjecture for the ideals in the Bernstein decomposition of H(G). The
conjecture says that each ideal is geometrically equivalent to an algebraic
variety. Our conjecture is closely related to Lusztig's conjecture on the
asymptotic Hecke algebra. We prove our conjecture for SL(2) and GL(n). We also
prove part (1) of our conjecture for the Iwahori ideals of the groups PGL(n)
and SO(5).
