This paper replaces 0828.
Let A be a regular noetherian Fp-algebra. The relative K-groups Kq(A[x]/(xm),(x)) and the Nil-groups Nilq(A[x]/(xm)) were evaluated by the author and Ib Madsen in terms of the big de Rham-Witt groups Wr&OmegaAq of the ring A. In this paper, we evaluate the maps of relative K-groups and Nil-groups induced by the canonical projection f : A[x]/(xm) &arr A[x]/(xn). The result depends strongly on the prime p. It generalizes earlier work by Stienstra on the groups in degree 2 and 3.