Hopf-theoretic approach to motives of twisted flag varieties.

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