dvi file and ps file.
For X a simply-connected finite H-space, there is a Bousfield-Kan spectral sequence which converges to the homotopy groups of its K-completion. When X=Spin(2n+1), we expect that these homotopy groups equal the v1-periodic homotopy groups of X in dimension greater than n^2. In this paper, we accomplish two things. (1) We prove that for any X, the 1-line of the spectral sequence is determined in an explicit way from the K-theory and Adams operations. (2) For X=Spin(2n+1), we make an explicit computation of this 1- line.