  We define and study an equivariant $E$-theory with respect to coactions of
Hopf $C^*$-algebras; we prove the Baaj-Skandalis duality in this setting. We
show that the corresponding equivariant $KK$-theory of Baaj and Skandalis
enjoys an universal property. In the appendix, we look at the different ways of
expressing equivariant stability for a functor, and prove an equivariant
Brown-Green-Rieffel stabilization result.
