Non-abelian Rees Construction and Motives

The classical Rees construction (of common use in commutative algebra and Hodge theory) interpolates between filtrations, viewed as Gm

-equivariant vector bundles on the affine line, and their associated gradings. Various non-abelian versions have been proposed, where Gm

is replaced by a reductive group. We shall present  a Galois correspondence between prehomogeneous spaces and certain monodical categories, and apply it to monoidal categories of motives with concrete applications to algebraic cycles.