Multiplicative K-theory and K-theory of functors (Q2390709)

There is a multiplicative \(K\)-theory \(K_{{\mathcal F}}(X)\) associated to a filtration \({\mathcal F}\) of the de Rham complex of a smooth manifold \(X\). The author shows that \(K_{{\mathcal F}}(X)\) is also the \(K\)-theory of an appropriate functor. Analogously, he demonstrates the equivalence of two possible constructions for the relative \(K\)-theory of a pair of manifolds.