SPLIT STRATA FOR A REDUCTIVE P-ADIC GROUP

We introduce, for a reductive p-adic group, a notion of split fundamen tal stratum of positive level playing the expected parr in the type th eory of Bushnell and Kutzko. in particular we prove that a smooth repr esentation containing such a stratum cannot be supercuspidal. The idea consists in deforming the stratum so that the Abelian character assoc iated with the deformed stratum will be contained in the representatio n and will verify a ''good'' intertwining formula. (C) Academie des Sc iences/Elsevier, Paris.