In the seminal paper "Unitaires multiplicatifs et dualité pour les produits croisés de $C^*$-algèbres" by Baaj and Skandalis, we find the following very general definition of what a corepresentation of a Hopf $C^*$-algebra (perhaps more properly called a "$C^*$-bialgebra") is:
There are no references given. I would justify the definition by using the isomorphism between $\mathcal L(H\otimes A)$ and $M(K(H)\otimes A)$, the latter algebra being where we usually take corepresentations to live.
I am interested in earlier, or contemporaneous, work which considers such a definition in more detail (or even just gives the definition).
That is, where does this definition come from? Is this the first paper to make it?