Motivic decomposition of anisotropic varieties of type F₄into generalized Rost motives

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 . We also establish a motivic isomorphism between two anisotropic non-isomorphic projective homogeneous varieties of type F 4 . All our results hold for Chow motives with integral coefficients.