### J-invariant of linear algebraic groups , by Victor Petrov , Nikita Semenov , and Kirill Zainoulline

Let G be a linear algebraic group over a field and X be a projective
homogeneous G-variety such that G splits over the function field of X. In the
present paper we introduce an invariant of G called J-invariant which
characterizes the splitting properties of the Chow motive of X. This
generalizes the respective notion invented by A.Vishik in the context of
quadratic forms. As a main application we obtain a uniform proof of all known
motivic decompositions of generically split projective homogeneous varieties
(Severi-Brauer varieties, Pfister quadrics, maximal orthogonal Grassmannians,
G_2- and F_4-varieties) as well as provide new ones (exceptional varieties of
types E_6, E_7 and E_8). We also discuss applications to canonical dimensions
and splitting properties of the group G.

Victor Petrov <kirill(at)mathematik.uni-muenchen.de >

Nikita Semenov <>

Kirill Zainoulline <>