This paper is a continuation of the paper [14], henceforth cited as I. Let k be a field of characteristic p ≥ 0 and k_s a separable closure of k. Let G/k be a semisimple simply connected algebraic group which is assumed absolutely almost k-simple, i.e. G *_k k_s is almost simple. Let g ∈ G(k) be an element of order n. The goal of the paper is to define and study an invariant M_G(g) with value in K_2(k)K_2(k), where K_2(k) denotes the second Milnor K-group of k. This invariant is characteristic-free and therefore it permits us to work in an arithmetical set-up.
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