THE GROTHENDIECK-RIEMANN-ROCH THEOREM FOR GROUP SCHEME ACTIONS

Let G be a group or a group scheme. We establish formulas for the equi variant Euler characteristic of locally free G-modules on a projective G-scheme: We prove an Adams-Riemann-Roch theorem and, under a certain continuity assumption for the push-forward map, a Grothendieck-Rieman n-Roch theorem in (higher) equivariant K-theory. Furthermore, we prese nt the following applications: The Adams-Riemann-Roch theorem implies that Adams operations and induction for representations commute with e ach other. In case of a flag variety G/B, the continuity assumption me ntionned above is verified, and the Grothendieck-Riemann-Roch theorem yields a new proof of the Weyl character formula. (C) Elsevier, Paris.