  Given a second-countable, locally compact group $G$, we consider amenable
$G$-actions on separable, stable, nuclear $\mathrm{C}^\ast$-algebras that are
isometrically shift-absorbing and tensorially absorb the trivial action on the
Cuntz algebra $\mathcal{O}_2$. We show that such actions are classified up to
cocycle conjugacy by the induced $G$-action on the primitive ideal space. In
the special case when $G$ is exact, we prove a unital version of our
classification theorem. For compact groups, we obtain a classification up to
conjugacy.
