The J-invariant is a discrete invariant of semisimple
algebraic groups which describes the motivic behavior of the variety of
Borel subgroups. This invariant was an important tool to solve several
long-standing problems. For example, it plays an important role in the
progress on the Kaplansky problem about possible values of the
u-invariant of fields by Vishik. In the talk I would like to present a
generalization of the J-invariant to groups of outer type and describe
some new combinatorial patterns for Chow groups and motives.