Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln

This article gives a selfcontained treatment of the theory of Kazhdan-Lusztig polynomials with special emphasis on affine reflection groups. There are only few new results but quite some new proofs. We close with a conjectural character formula for tilting modules, which formed the starting point of these investigations. As a later addition, we include a brief treatment of Lusztig's new periodic W-graphs.