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A connection between the indices of the Tits algebras of a split linearalgebraic group G and the degree one parameters of its motivic J-invariant wasintroduced by Queguiner-Mathieu, Semenov and Zainoulline through use of thesecond Chern class map in the Riemann-Roch theorem without denominators. Inthis paper we extend their result to higher Chern class maps and provideapplications to groups of inner type E6.

The J-invariant and Tits algebras for groups of inner type E6