  K. Hess's theory of homotopical descent, applied to the large categories of
motives defined recently by Blumberg, Gepner, and Tabuada, suggests that the
Koszul dual of Waldhausen's K-theory of the sphere spectrum, regarded as a
supplemented algebra via the Dennis trace, plays a very general role as a kind
of motivic group.
  After tensoring with the rationals, the resulting Hopf algebra has close
relations to the ring of quasi-symmetric functions and work of Baker and
Richter on one hand, and on the other to work of Deligne and others on the
motivic group for mixed Tate motives.
