Non connective K-theory via universal invariants

In this article, we further the study of higher K-theory of dg categories via universal invariants, initiated by the second named author. Our main result is the co-representability of non-connective K-theory by the base ring in the universal localizing motivator. As an application, we obtain for free higher Chern characters, resp. higher trace maps, e.g. from non-connective K-theory to cyclic homology, resp. to topological Hochschild homology.