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Soit G un groupe algebrique reductif sur la cloture algebrique d'un corpsfini F_q et defini sur ce dernier. L'existence du support unipotent d'uncaractere irreductible du groupe fini G(F_q), ou d'un faisceau caractere de G,a ete etablie dans differents cas par Lusztig, Geck et Malle, et le secondauteur. Dans cet article, nous demontrons que toute classe unipotente surlaquelle la restriction du faisceau caractere ou du caractere donne est nonnulle est contenue dans l'adherence de Zariski de son support unipotent. Pouretablir ce resultat, nous etudions certaines representations des groupes deWeyl, dites "bien supportees".  Let G be a reductive algebraic group over the algebraic closure of a finitefield F_q that is defined over F_q. Under various conditions, Lusztig, Geck andMalle, and the second author have shown that an irreducible character of thefinite group G(F_q), or a character sheaf on G, has a unipotent support. Inthis paper, we show that every unipotent class on which a given character orcharacter sheaf has nonzero restriction is contained in the Zariski closure ofits unipotent support. This result is obtained by studying the class ofso-called "well-supported" representations of Weyl groups.

SUPPORTS UNIPOTENTS DE FAISCEAUX CARACTÈRES