Alexander Neshitov: Motives and oriented cohomology of a linear algebraic group

Submission: 2013, Jul 14

For a cellular variety X and an algebraic oriented cohomology theory h of Levine-Morel we construct a filtration on the cohomology ring h(X) such that the associated graded ring is isomorphic to the Chow ring of X. Taking X to be the variety of Borel subgroups of a split semisimple linear algebraic we apply this filtration to relate the oriented cohomology of the group to its Chow ring. As an immediate application we compute the algebraic cobordism ring of a group of type G_2, of groups SO_n and Spin_m for n=3,4 and m=3,4,5,6 and PGL_k for k>1. Using this filtration we also establish some comparison result between Chow motives and h-motives of generically cellular varieties.

2010 Mathematics Subject Classification: 20G10

Keywords and Phrases: Oriented cohomology, motives, flag varieties

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