Let G be a split semisimple algebraic group over an arbitrary field F , let E be a G-torsor over F , and let P be a parabolic subgroup of G. The quotient variety X := E/P , known as a flag variety, is generically split, if the parabolic subgroup P is special. It is generic, provided that the G-torsor E over F is a standard generic G k -torsor for a subfield k ⊂ F and a split semisimple algebraic group G k over k with (G k )F = G.For any generically split generic flag variety X, we show that the Chow ring CH X is generated by Chern classes (of vector bundles over X). This implies that the topological filtration on the Grothendieck ring of X coincides with the computable gamma filtration. The results were already known in some cases including the case where P is a Borel subgroup.We also provide a complete classification of generically split generic flag varieties and, equivalently, of special parabolic subgroups for split simple groups.Contents 497 any P -torsor over any extension field of the base field is trivial. This is equivalent to the fact that the generic flag variety X := E/P is generically split, see Lemma 7.1.In the present paper, we show that a generically split generic flag variety X = E/P has the same property as in the above particular case with P = B: the topological filtration on the Grothendieck ring K(X) coincides with the gamma filtration. This confirms that the introduced by Grothendieck gamma filtration is a good approximation of the topological filtration. And not only in the well-known sense that they both coincide after tensoring by Q.The reason for this coincidence (with Z-coefficients) is our main result (Theorem 7.3) saying that the ring CH X coincides with its Chern subring. In its turn, Theorem 7.3 is a consequence of the similar statement for the Chow ring of the classifying space of P , see Proposition 5.5.The assumption that P is special is essential. For instance, taking for G a spinor group Spin(n), we may take a parabolic subgroup P ⊂ G such that the variety X = E/P is a projective quadric. Then the gamma filtration on K(X) is different from the topological filtration provided that n 9. Indeed, as shown in [9], the component of codimension 2 of the graded ring associated with the gamma filtration contains an element of order 2; on the other hand, by [8, Theorem 6.1 and § 3.1], the component of codimension 2 of the graded ring associated with the topological filtration is torsion-free for such n.For an overview of sections of the paper we refer to the table of contents: the titles of sections are self-explaining. Note that the paper ends with a classification of special parabolic subgroups (or, equivalently, of generically split generic flag varieties).