  Let X be a geometrically split, geometrically irreducible variety over a
field F satisfying Rost nilpotence principle. Consider a field extension E/F
and a finite field K. We provide in this note a motivic tool giving sufficient
conditions for so-called outer motives of direct summands of the Chow motive of
X_E with coefficients in K to be lifted to the base field. This going down
result has been used S. Garibaldi, V. Petrov and N. Semenov to give a complete
classification of the motivic decompositions of projective homogeneous
varieties of inner type E_6 and to answer a conjecture of Rost and Springer.
