Have a look on the paper

F. Morel, Voevodsky's proof of Milnor's conjecture, Bull. Amer. Math. Soc. 35 (1998), 123-143, doi:10.1090/S0273-0979-98-00745-9.

and go to example 6.5 please.

In this article Morel writes that the Rost-Motive of a n-fold Pfister quadric $M_\alpha$ = $M(spec(L))$ for n=1 and for n=2 it coincides with the motive of a conic. He then writes that for n > 2 this is no longer true, meanig that the Rost-Motive is not the motive of a algebraic variety (as far as i understand him).

Where can i find an example for this? Is there some general reason why this happens?

Thank you.