  We introduce an equivariant version of the weak expectation property (WEP) at
the level of operator modules over completely contractive Banach algebras $A$.
We prove a number of general results---for example, a characterization of the
$A$-WEP in terms of an appropriate $A$-injective envelope, and also a
characterization of those $A$ for which $A$-WEP implies WEP. In the case of
$A=L^1(G)$, we recover the $G$-WEP for $G$-$C^*$-algebras in recent work of
Buss--Echterhoff--Willett. When $A=A(G)$, we obtain a dual notion for operator
modules over the Fourier algebra. These dual notions are related in the setting
of dynamical systems, where we show that a $W^*$-dynamical system
$(M,G,\alpha)$ with $M$ injective is amenable if and only if $M$ is
$L^1(G)$-injective if and only if the crossed product $G\bar{\ltimes}M$ is
$A(G)$-injective. Analogously, we show that a $C^*$-dynamical system
$(A,G,\alpha)$ with $A$ nuclear and $G$ exact is amenable if and only if $A$
has the $L^1(G)$-WEP if and only if the reduced crossed product $G\ltimes A$
has the $A(G)$-WEP.
