The talk is based on a joint work with A. Neshitov, N. Semenov, V. Petrov (arXiv:1505.07083). Following the motivic Galois group approach we relate a subcategory generated by the oriented motive of a versal flag variety with the category of integer/modular representations of certain Hecke-type algebras. As an application, we describe irreducible blocks of the affine nil-Hecke algebra (over a finite field of characteristic dividing the order of the Weyl group) using recent results on motives of twisted flag varieties.