Chow motives of twisted flag varieties

Let G be an adjoint simple algebraic group of inner type. We express the Chow motive (with integral coefficients) of an anisotropic projective G-homogeneous variety 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 SB2(A) of a division algebra A of degree 5 into a direct sum of twisted motives of the Severi-Brauer variety SB(B) of a division algebra B Brauer-equivalent to the tensor square A(x2). As an application we provide another counter-example to the uniqueness of a direct sum decomposition in the category of motives with integral coefficients.