Hecke algebras associated with induced representations

We define the Hecke von Neumann algebra L(G, H, sigma) associated with a group G, a subgroup H and a unitary representation sigma of H. We show that when sigma is finite dimensional, L (G, H, sigma) can be seen as a corner algebra of the tensor product of the group von Neumann algebra of a locally compact group and a matrix algebra. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.