Some evidence for the existence of Ulrich bundles

The question of existence of Ulrich bundles on nonsingular projective varieties is posed here in weaker terms: either to find a K-theoretic solution, or to find one in the derived category of the variety. We observe that if any motivic vector bundle is algebraic, there is always a solution in the Grothendieck group. Also, by considering the derived problem, it is noted a formal way of producing Ulrich sheaves on a surface.