Hecke algebras associated with induced representations

We define the Hecke von Neumann algebra L(G,H,σ) associated with a group G, a subgroup H and a unitary representation σ of H. We show that when σ is finite dimensional, L(G,H,σ) 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