Character formulas for tilting modules over Kac-Moody algebras

We show how to express the characters of tilting modules in a (possibly parabolic) category O over a Kac-Moody algebra in terms of the characters of simple highest weight modules. This settles in lots of cases Conjecture 7.2 of my preprint "Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln" describing the characters of tilting modules for quantum groups at roots of unity.