univ\] Let $\bB$ be a bivariant theory on $\m V$ such that a smooth morphism $f: X\to Y$ has a stable orientation $\theta(f)\in \bB(f)$. Then there exists a unique Grothendieck transformation $$\ga:=\ga_{\theta}: \bM(\m V/-) \to \bB(-)$$ satisfying the normalization condition that for a smooth morphism $f:X \to Y$ the following identity holds in $\bB(X \xrightarrow {f} Y)$: $$\ga([X \xrightarrow {\op {id}_X} X]) =  \theta(f).$$  Let $c\ell: Vect(-) \to  \bB^*(-)$ be a contravariant functorial characteristic class of algebraic (or analytic) vector bundles with values in the associated cohomology theory, which is multiplicative in the sense that $c\ell(V) = c\ell(V') c\ell(V'')$ for any short exact sequence of vector bundles $0\to V'\to V \to V'' \to 0$, with $c\ell(T_{pt})=0_{pt}\in \bB^*(\{pt\})$. Assume that $c\ell$ commutes with the stable orientation $\theta$, i.e. $$\theta(f)\bullet cl(V)=f^*cl(V)\bullet \theta(f)$$ for all smooth morphism $f: X\to Y$ and $V\in Vect(Y)$. Then there exists a unique Grothendieck transformation $$\ga_{c\ell}: \bM(\m V/-) \to \bB(-)$$ satisfying the normalization condition that for a smooth morphism $f:X \to Y$ the following identity holds in $\bB(X \xrightarrow {f} Y)$: $$\ga_{c\ell}([X \xrightarrow {\op {id}_X} X]) = c\ell(T_f) \bullet \theta(f).$$ Here $T_f$ is the relative tangent bundle of the smooth morphism $f$.  This follows from Theorem \[