Let Vect_n be the moduli stack of vector bundles of rank n on derived schemes. We prove that, if E is a Zariski sheaf of ring spectra which is equipped with finite quasi-smooth transfers and satisfies projective bundle formula, then E^⁎(Vect_n,S) is freely generated by Chern classes c₁,…,c_n over E^⁎(S) for any qcqs derived scheme S. Examples include all multiplicative localizing invariants.