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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. Résumé. -Dans cet article nous démontrons une formule dedoi:10.5802/ahl.79 fatcat:lgbp2zzcdjc57jhbarz56g23au