Embeddings of Hecke algebras in group algebras (Q1084493)

For G a finite group and B a subgroup the Hecke algebra H(G,B) is the endomorphism algebra of the induced permutation \(Ind^ G_ B(1)\). When \(| B|\) is invertible in the field K, there is a canonical embedding of H(G,B) in the group ring KG. If G is a finite Chevalley group over a field of characteristic p and B is a Borel subgroup of G, then there is a canonical embedding of \(H_ R(G,B)\) in the group ring RG where R is any commutative ring in which \(| \cap_{w\in W}B^ w|\) is invertible.