Canonical Nonclassical Hopf-Galois Module Structure of Nonabelian Galois Extensions

Let $L\mathrm{/}K$ be a finite Galois extension of local or global fields in characteristic $0$ or $p$ with nonabelian Galois group $G$, and let ${\mathfrak B}$bea$G$-stablefractionalidealof$L$\mathrm{.}Weshowthat${\mathfrak B}$ is free over its associated order in $K[G]$ if and only if it is free over its associated order in the Hopf algebra giving the canonical nonclassical Hopf-Galois structure on the extension.