Hopf-theoretic approach to motives of twisted flag varieties

Abstract

Let $G$ be a split semisimple algebraic group over a field and let $A^{\ast }$ be an oriented cohomology theory in the sense of Levine--Morel. We provide a uniform approach to the $A^{\ast }$-motives of geometrically cellular smooth projective $G$-varieties based on the Hopf algebra structure of $A^{\ast }(G)$. Using this approach we provide various applications to the structure of motives of twisted flag varieties.

33 pages

References in corpus (4)

• Algebraic cobordism
• Fast generalized Bruhat decomposition
• Chern classes from Morava K-theories to $p^n$-typical oriented theories
• Rost nilpotence and free theories