  For a regular ring R and an affine monoid M the homotheties of M act
nilpotently on the Milnor unstable groups of R[M]. This strengthens the K_2
part of the main result of [G5] in two ways: the coefficient field of
characteristic 0 is extended to any regular ring and the stable K_2-group is
substituted by the unstable ones. The proof is based on a
polyhedral/combinatorial techniques, computations in Steinberg groups, and a
substantially corrected version of an old result on elementary matrices by
Mushkudiani [Mu]. A similar stronger nilpotence result for K_1 and algorithmic
consequences for factorization of high Frobenius powers of invertible matrices
are also derived.
