In this article, we further the study of higher K-theory of differential graded (dg) categories via universal invariants, initiated in [G. Tabuada, Higher K-theory via universal invariants, Duke Math. J. 145 (2008), 121–206]. 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, respectively higher trace maps, from non-connective K-theory to cyclic homology, respectively to topological Hochschild homology.