Units of ring spectra and their traces in algebraic K-theory

Let GL_1® be the units of a commutative ring spectrum R. In this paper we identify the composition BGL_1®->K®->THH®->\Omega^{\infty}®, where K® is the algebraic K-theory and THH® the topological Hochschild homology of R. As a corollary we show that classes in \pi_{i-1}® not annihilated by the stable Hopf map give rise to non-trivial classes in K_i® for i\geq 3.