Motivic decomposition of anisotropic varieties or type F-4 into generalized Rost motives

摘要

We prove that the Chow motive of an anisotropic projective homogeneous variety of type F-4 is isomorphic to the direct sum of twisted copies of a generalized Rost motive. In particular, we provide an explicit construction of a generalized Rost motive for a generically splitting variety for a symbol in K-3(M)(k)/3. We also establish a motivic isomorphism between two anisotropic non-isomorphic projective homogenous varieties of type F-4. All our results hold for Chow motives with integral coefficients.