Motivic strict ring spectra representing semi-topological cohomology theories

We show that Shipley's "detection functor" for symmetric spectra generalizes to motivic symmetric spectra. As an application, we construct motivic strict ring spectra representing morphic cohomology, semi-topological K-theory, and semitopological cobordism for complex varieties. As a further application to semi-topological cobordism, we show that it is related to semi-topological K-theory via a Conner-Floyd type isomorphism and that after inverting a lift of the Friedlander-Mazur s-element in morphic cohomology, semi-topological cobordism becomes isomorphic to periodic complex cobordism.