  In this paper we prove a character formula expressing the classes of simple
representations in the principal block of a simply-connected semisimple
algebraic group G in terms of baby Verma modules, under the assumption that the
characteristic of the base field is bigger than 2h-1, where h is the Coxeter
number of G. This provides a replacement for Lusztig's conjecture, valid under
a reasonable assumption on the characteristic.
