maybe this question is trivial and, then this is the reason I've never seen this written.

The motivation is to define internal $\infty$-groupoids (that are preferably) Kan fibrant and to see if Kan fibrancy is really a necessary ontological assumption. As I understand there are non-Kan fibrant models of smooth $\infty$-groupoids given by $\infty$-stacks over cartesian spaces (http://ncatlab.org/nlab/show/smooth+infinity-groupoid), however there are Kan fibrant versions for the smooth case too (http://ncatlab.org/nlab/show/Kan-fibrant+simplicial+manifold)

So the questions are more or less:

1. Given a (closed) monoidal (model) category $\mathcal{V}$, is there an operad (that I will call $\text{Grpd}$) such that algebras over $\text{Grpd}$ are exactly the internal groupoids?

2)If the answer to 1) is yes. Let $\text{Grpd}_{\infty}$ be the resolutions of $\text{Grpd}$. What's a $\text{Grpd}_{\infty}$-algebra?

Thanks in advance