Let (G,S) be a Hecke pair, i.e., G is a group and S an almost normal subgroup, meaning that every double coset SgS is the union of finitely many left cosets of S. We show that there exists a homomorphism ϕ from G to a totally disconnected, locally compact group G̃ such that S̃ := (S) is a compact, open subgroup of G̃, and such that the Hecke algebras H(G,S) and H(G̃,S̃) are isomorphic. This "topologization" construction is then used to solve a problem in the theory of Hecke C*-algebras.
2002 Spring Topology and Dynamics Conference. Proceedings of the 2002 Spring Topology and Dynamics Conference [presented in Topology Proceedings, Vol. 26, No. 2] (Austin, TX 21-23 March, 2002) p. 565-591