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

**EDIT**: Apparently, there's a misunderstanding regarding the notion of operad as noticed by Todd Trimble in the comments (I didn't know about this notation issues). I'm assuming the definition of operad given from page 23 to 30 of http://www.cs.ox.ac.uk/people/bob.coecke/andrei.pdf

couldstretch the meaning of operad so that a Lawvere theory is a "cartesian operad". But then that stretch should be made clear in the question!) $\endgroup$ – Todd Trimble♦ Oct 1 '15 at 18:52