Let \(\iota: A \hookrightarrow B\) be a faithful \(G\text{-embedding}\). The following are equivalent:

1. \(\iota \rtimes_{\max} G: A \rtimes_{\max} G \to B \rtimes_{\max} G\) is injective;
2. for any covariant representation \((\pi, u) : (A,G) \to \mathbb{B}(H)\), there is a ccp \(G\text{-map}\) \(\phi:B \to \mathbb{B}(H)\) with \(\phi \circ \iota = \pi\);
3. there exists a covariant representation \((\pi, u): (A,G) \to \mathbb{B}(H)\) such that the integrated form \(\pi \rtimes u: A \rtimes_{\max} G \to \mathbb{B}(H)\) is faithful and for which there is a ccp \(G\text{-map}\) \(\phi:B \to \mathbb{B}(H)\) with \(\phi \circ \iota = \pi\);

Buss, Willet, and Echterhoff “Injectivity, crossed products, and amenable group actions.”