  This an extended version of the previous preprint dated by February 2005.
  We prove that the Chow motive of an anisotropic projective homogeneous
variety of type F4 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 homogeneous varieties of type F4. All our results
hold for Chow motives with integral coefficients.
