We introduce a generalized version of a q-Schur algebra (of parabolic type) for arbitrary Hecke algebras over extended Weyl groups. We describe how the de¬ composition matrix of a finite group with split BN-pair, with respect to a non-describing prime, can be partially described by the decomposition matrices of suitably chosen q-Schur algebras. We show that the investigated structures occur naturally in finite groups of Lie type.

In modular representation theory of a finite group the theory of Green vertices plays an important role. In the representation theory of finite groups with split BN-pairs Harish-Chandra induction has become one of the most important tools in the last decades. This paper will show how the combination of both gives new insight into the modular representation theory of these groups. ᮊ

No abstract