 so that the canonical projection $\bB q: \bM(\m V/-) \to \bK_0(\m V / - )$ is a Grothendieck transformation.  0.  There exists a unique Grothendieck transformation $$mC_y=\La_y^{mot}: \bK_0(\m V_k^{qp}/ - ) \to \bK_{alg}( - )\otimes \bZ[y]$$ satisfying the normalization condition that for a smooth morphism $f: X \to Y$ the following equality holds in $\bK_{alg}(X \xrightarrow {f} Y) \otimes \bZ[y]$: $$\La_y^{mot}\Bigl(\Bigl[[X  \xrightarrow{\op {id}_X}  X]\Bigr]\Bigr) = \La_y(T^*_f) \bullet 