Submission: 2011, May 30
In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the J-invariant of E and in the case of Grothendieck's K_0 indexes of the respective Tits algebras.
2010 Mathematics Subject Classification: Primary 20G15; Secondary 19L47, 14F43
Keywords and Phrases: torsor, equivariant cohomology, Rost cycle module
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