A norm homomorphism for the group of R-equivalence classes of all simply connected semisimple classical algebraic groups is constructed. The group of Ž . R-equivalence classes for special unitary groups SU B, is computed. It is proved Ž . Ž . that the variety of SU B, is rational if ind B F 3 and the stable birational type Ž . of SU B, depends only on the Brauer class of B and does not depend on the involution . ᮊ 1998 Academic Press
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The notion of R-equivalence, introduced by Manin in 11 , is an important birational invariant of an algebraic variety defined over an arbitrary field F. In the case of an algebraic group G the set of R-equivalence Ž . classes G F rR has a natural group structure, which was studied by w x Colliot-Thelene and Sansuc in 5 .
´Let G be a connected algebraic group defined over a field F. The group G is called rational if the variety of G is rational; i.e., G is birationally isomorphic to an affine space. We call G stably rational if the variety G = ށ n is rational for some n. If a connected algebraic group G, defined F over F, is a direct factor of a stably rational group, then the group G is Ž . R-tri¨ial; i.e., the group of R-equivalence classes G L rR is trivial for any