  Let $A$ be a Hopf algebra over a field $K$ of characteristic zero such that
its coradical $H$ is a finite dimensional sub-Hopf algebra. Our main theorem
shows that there is a gauge transformation $\zeta $ on $A$ such that
$A^{\zeta}\cong Q#H$ where $A^\zeta$ is the dual quasi-bialgebra obtained from
$A$ by twisting its multiplication by $\zeta$, $Q$ is a connected dual
quasi-bialgebra in $^H_H\mathcal{YD}$ and $Q #H $ is a dual quasi-bialgebra
called the bosonization of $Q$ by $H$.
