 Iwahori-Hecke algebra of a BN-pair

This is a finite-group realization of an Iwahori-Hecke algebra. For a finite group $G$ with a BN-pair, the Iwahori-Hecke algebra over $k$ is the endomorphism algebra of the permutation module $k[G/B]$, up to the conventional opposite algebra. Its standard basis is indexed by the Bruhat double cosets.