 Our construction of the Grothendieck transformation $$mC_y=\La_y^{mot}: \bK_0(\m V_k^{qp}/ - ) \to \bK_{alg}( - )\otimes \bZ[y]$$ based on [@Gros Chapter IV, Theorem 0.0.0 and (0.0.0)] also works in the algebraic context without considering only quasi-projective varieties, if one uses the more sophisticated definition of $\bK_{alg}(X \xrightarrow {f} Y)=K_0(D^b_{f-perf}(X))$ as the Grothendieck goup of the triangulated category of $f$-perfect complexes. And a similar definition can also be used in the context of compact complex analytic varieties (c