Motives of reductive groups (Q2879630)

In this interesting and nicely written paper the author determines the structure of the rationalized geometric motive of a split reductive algebraic group over a perfect field. The main result shows that the motive of a reductive group is isomorphic to a symmetric product of certain weighted cohomology vector spaces of given dimensions. This is the avatar for results in cohomology or any other contravariant theory in which this isomorphism turns into the familiar description using alternating algebras. In particular, this generalizes previous work on the cohomology and pure Chow motives of reductive groups. The article ends with explicit calculations of the motives of classical algebraic groups.