We show a Springer type theorem for the variety of parabolic subgroups of type 1, 2, 6 for all groups of type \(\textrm{E}_6\) . As far as we know this gives the first example for the validity of the Springer theorem for projective homogeneous varieties of type \(^2\textrm{E}_6\) different from varieties of Borel subgroups. The proof combines several topics, notably the Rost invariant, a Tits construction, Cartan’s symmetric spaces and indirectly the structure of the Chow motives of projective homogeneous varieties of exceptional type.
