This question is already posted in math.stackexchange, but didn't receive any answer. I'm not sure if this question fits in here, but surely someone in here can guide me to the correct answer.

To make things as simple as possible, let's say we have a discrete group $G$. 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?