Submission: 2005, Feb 17
We provide an explicit decomposition of the motives of two anisotropic projective homogeneous varieties of type F4. In particular, we provide an explicit construction of a generalized Rost motive for a norm variety that corresponds to a symbol (3,3). We also establish a motivic isomorphism between two projective homogeneous varieties of type F4. We provide an explicit construction of this isomorphism. All our proofs work for Chow motives with integral coefficients.
2000 Mathematics Subject Classification: 14C15, 57T15
Keywords and Phrases: anisotropic homogeneous variety, Rost motive, exceptional algebraic group
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