by A. S. Merkurjev, I. A. Panin, and A. R. WadsworthThis is preprint 94 - 079 of the Universitaet Bielefeld preprint series (Preprintreihe Sonderforschungsbereich 343 "Diskrete Strukturen in der Mathematik").
In this preprint, we give without proofs a list of the index reduction formulas for all the projective varieties X such that there is an action of a simple classical group G on X over the ground field F, such that the action becomes transitive over the separable closure of F. We cover groups of both inner and outer type. Proofs of the formulas can be found in the preprints Index Reduction Formulas for Twisted Flag Varieties I, II, by the same authors, which are available here and from the K-theory Archive.