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

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Let GL₁(R) be the units of a commutative ring spectrum R. In this paper we identify the composition BGL₁(R)->K(R)->THH(R)->Ω∞(R), where K(R) is the algebraic K-theory and THH(R) the topological Hochschild homology of R. As a corollary we show that classes in πᵢ₋₁(R) not annihilated by the stable Hopf map give rise to non-trivial classes in Kᵢ(R) for i≥ 3.