This preprint was accepted March 29, 2004
ABSTRACT: The paper can be considered as an addendum to a paper of Thomason and Throbaugh where K-theory of algebraic varieties is equipped with relative K-groups. It is proved that this enriched K-theory satisfies the Panin-Smirnov axioms for ring cohomology theories of algebraic varieties. In particular it is proved that the Leibnitz formula, describing an interaction between a multiplication and a differential, holds in this case. A language of symmetric spectra and of monoidal model categories is used.[Full text: (.ps.gz)]