Over the last decade Nikita Semenov, Skip Garibaldi and others have made some progress in the theory of cohomological invariants, (Rost)-motives and motivic decompositions of algebraic groups. For example a motivic decomposition of $F_4/P$, with $P$ being a certain parabolic subgroup has been established by Semenov, Nikolenko and Zainoulline.

Looking at the Dynkin diagramm of $D_n$ one will notice that the case $n=4$ gives a diagramm with a special symmetry (cue: triality).

Question: Is the symmetry of the Dynkin diagramm of $D_4$ somehow reflected in the motive of $D_4$ or is there a motivic decomposition known at all?

It might be possible that the motivic structure can be derived from general results, but i dont too many papers dealing with these kinds of problems.