Isocrystals with additional structure. II

Let F be a p -adic field, let L be the completion of a maximal unramified extension of F , and let σ be the Frobenius automorphism of L over F . For any connected reductive group G over F one denotes by $B(G)$ the set of σ -conjugacy classes in $G(L)$ (elements $x,y$ in $G(L)$ are said to be σ -conjugate if there exists g in $G(L)$ such that g⁻1 κ σ(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).