A two-sided q-analogue of the Coxeter complex
Markus Linckelmann and Sibylle Schroll

Abstract. We define a complex of bimodules over the Iwahori-Hecke 
algebra associated to a finite Coxeter group, calculate its
cohomology and show that it induces a derived equivalence over
its module category extending the Morita equivalence given by a
certain algebra automorphism. We show further that when tensored
with the index representation this complex becomes isomorphic to
the one-sided q-analogue of the Coxeter complex previously defined
by V. Deodhar [Deo] and A. Mathas [Ma].