  We introduce the notion of an action of a discrete or compact quantum group
on an operator system, and study equivariant operator system injectivity. We
then prove a duality result that relates equivariant injectivity with dual
injectivity on associated crossed products. As an application, we give a
description of the equivariant injective envelope of the reduced crossed
product built from an action of a discrete quantum group on an operator system.
