Submission: 2004, Jul 16, updated: 2005, Jan 4
In this paper we compute Grothendieck-Witt and Witt groups of representation categories of split reductive algebraic groups. We also define transfer maps between Witt groups with respect to proper morphisms and establish the base change and projection formulae for those. Then we use the to define the cateory of Witt motives In forthcoming work, these results will hopefully be improved and combined to lead to the computation of Witt groups of twisted flag varietes.
This updated version contains an appendix explaining how to deal with sign computations using adjunctions.
2000 Mathematics Subject Classification: 11E81, 11E39, 18E30, 19G12, 20G05
Keywords and Phrases: Witt groups, representations of reductive algebraic groups, motives, Grothendieck duality
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