Isocrystals with additional structure .2.

Let F be a p-adic field, let L be the completion of a maximal unramified extension of F, and let a be the Frobenius automorphism of L over F. For any connected reductive group G over F one denotes by B(G) the set of a-conjugacy classes in G(L) (elements x, y in G(L) are said to be a-conjugate if there exists g in G(L) such that g(-1)kappa sigma(g) = y. One of the main results of this paper is a concrete description of the set B(G) (previously this was known only in the quasi-split case).