  In this paper we use ideas of the non-abelian Iwasawa main conjecture to
prove a result about the first Galois cohomology of continuous Galois modules
V_p(j) for large Tate-twist j and V_p a Q_p vector space. We show that under a
technical hypothesis that H^1(K, V_p(j)) is generated by twists of
norm-compatible units in an infinite tower of number fields with elements in
V_p(j-1). This confirms a consequence of the non-abelian Iwasawa main
conjecture. Using the "Bloch-Kato-conjecture" a similar result is proven for
motivic cohomology with finite coefficients.
