A weak expectation property for operator modules, injectivity and amenable actions

We introduce an equivariant version of the weak expectation property (WEP) at level operator modules over completely contractive Banach algebras [Formula: see text]. prove a number general results — for example, characterization text]-WEP in terms appropriate text]-injective envelope, and also those text] which implies WEP. In case text], we recover text]-[Formula: text]-algebras recent work Buss–Echterhoff–Willett [A. Buss, S. Echterhoff R. Willett, The maximal injective crossed product, to appear Ergodic Theory Dynam. Systems, https://doi.org/10.1017/etds.2019.25 ]. When obtain dual notion Fourier algebra. These notions are related setting dynamical systems, where show that text]-dynamical system with is amenable if only product text]-injective. Analogously, nuclear exact has reduced text]-WEP.