Does anyone know of a point-set level model for complex K-theory as a commutative ring spectrum?

For real $K$-theory I know of "A symmetric ring spectrum representing KO-theory" by Michael Joachim (Topology, 40(2) 2001).

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Does anyone know of a point-set level model for complex K-theory as a commutative ring spectrum?

For real $K$-theory I know of "A symmetric ring spectrum representing KO-theory" by Michael Joachim (Topology, 40(2) 2001).

kuandKUas commutative rings in symmetric spectra. $\endgroup$ – Arun Debray Jun 16 at 4:44