To male thinks simple as possible, lets say we have a discrete group $G.$ Then the then the group algebra $\mathbb{C}[G]$ (of finitely supported complex valued functions on $G$) has a convolution and an involution operation given by $$(f\star g)(x)=\sum_{x=ab}f(a)g(b), \qquad f^{\ast}(x)=\overline{f(x^{-1})}$$
It is easier to interpret $\mathbb{C}[G]$ as the free complex vector space spanned by $G$ for notational convenience. I came across a statement that says this $\ast$-convolution algebra has a natural Hopf algebra structure given by comultiplication $\Delta(g)=g\otimes g$ and counit $\epsilon(g)=1,$ then extended linearly. Also antipode is given by $\ast$-operation extended antilinearly.
Now I would like to know, what happen if we replace the group $G$ with a groupoid? My naïve guess is that we would get a Hopf algebroid (many object analogue of the known construction). If it is the case, how would the coalgebra look like? Can anyone explain me this structure or direct me to a (simple) reference?
This question is cross posed on MO and received a positive answer.