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Let $L/K$ be a finite Galois extension of local or global fields incharacteristic $0$ or $p$ with nonabelian Galois group $G$, and let ${\mathfrakB}$ be a $G$-stable fractional ideal of $L$. We show that ${\mathfrak B}$ isfree over its associated order in $K[G]$ if and only if it is free over itsassociated order in the Hopf algebra giving the canonical nonclassicalHopf-Galois structure on the extension.

Canonical Nonclassical Hopf-Galois Module Structure of Nonabelian Galois Extensions