Cellularity of endomorphism algebras of tilting objects

We show that, in a highest weight category with duality, the endomorphism algebra of tilting object is naturally cellular algebra. Our proof generalizes recent construction Andersen, Stroppel, and Tubbenhauer [4] . This result raises question whether all algebras can be realized this way. The also works without presence duality yields standard bases, sense Du Rui, which have similar combinatorial features to bases. As an application, we obtain bases—and thus general theory “cell modules”—for Hecke associated finite complex reflection groups (as introduced by Broué, Malle, Rouquier) via O rational Cherednik For real these bases are cellular.