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