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Submission: 2005, May 11
Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of some anisotropic projective G-homogeneous varieties in terms of motives of simpler G-homogeneous varieties, namely, those that correspond to maximal parabolic subgroups of G. We decompose the motive of a generalized Severi-Brauer variety SB_2(A), where A is a division algebra of degree 5, into a direct sum of two indecomposable motives. As an application we provide another counter-example to the uniqueness of a direct sum decomposition in the category of motives with integral coefficients.
2000 Mathematics Subject Classification: 20G15, 14F42
Keywords and Phrases: anisotropic homogeneous variety, twisted flag variety, Chow motive, generalized Severi-Brauer variety
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