  A connection between the indices of the Tits algebras of a split linear
algebraic group G and the degree one parameters of its motivic J-invariant was
introduced by Queguiner-Mathieu, Semenov and Zainoulline through use of the
second Chern class map in the Riemann-Roch theorem without denominators. In
this paper we extend their result to higher Chern class maps and provide
applications to groups of inner type E6.
