Geodesic
On classification of projective homogeneous varieties up to motivic isomorphism
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 158-172

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We give a complete classification of anisotropic projective homogeneous varieties of dimension less than 6 up to motivic isomorphism. We give several criterions for anisotropic flag varieties of type $\mathrm{A}_n$ to have isomorphic motives. 
@article{ZNSL_2006_330_a8,
     author = {K. V. Zainullin and N. S. Semenov},
     title = {On classification of projective homogeneous varieties up to motivic isomorphism},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {158--172},
     publisher = {mathdoc},
     volume = {330},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a8/}
}
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K. V. Zainullin; N. S. Semenov. On classification of projective homogeneous varieties up to motivic isomorphism. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 158-172. http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a8/