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

Classification of equivariantly $\mathcal{O}_2$-stable amenable actions on nuclear $\mathrm{C}^\ast$-algebras