  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.
