  This is a revision of a McMaster University preprint, with extension.
  In this paper we prove that over local or global fields of characteristic 0,
the Corestriction Principle holds for kernel and image of all maps which are
connecting maps in group cohomology and the groups of $R$-equivalences. Some
related questions over arbitrary fields of characteristic 0 are also discussed.
  AMS Mathematics Subject Classification (1991): Primary 11E72, Secondary
18G50, 20G10
