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Let $G$ be a split semisimple algebraic group over a field and let $A^*$ bean oriented cohomology theory in the sense of Levine--Morel. We provide auniform approach to the $A^*$-motives of geometrically cellular smoothprojective $G$-varieties based on the Hopf algebra structure of $A^*(G)$. Usingthis approach we provide various applications to the structure of motives oftwisted flag varieties.

Hopf-theoretic approach to motives of twisted flag varieties