K-theory for analytic spaces

We introduce a version of algebraic K-theory and related localising invariants for bornological algebras, using Efimov's recently introduced continuous K-theory. In the commutative setting, our invariant satisfies descent for various topologies that arise in analytic geometry (defined using bornological algebras). If time permits, I will also discuss a version of the Grothendieck-Riemann-Roch Theorem for analytic spaces.