I know that the Cuntz algebras $\mathcal{O}_n$, $n=1,2,...,\infty$, have groupoid models. I.e. they can be realised as groupoid C*-algebras. Can you describe the standard groupoid model for $\mathcal{O}_n$ or direct me towards relevant literature?

I believe it was first done 43 years ago in [1] in what seems to be a complicated way. Perhaps there is a better way now. Or may be it has been explained in a bite-sized manner in some lecture notes.

[1]

Renault, Jean, A groupoid approach to C*-algebras, Lecture Notes in Mathematics. 793. Berlin-Heidelberg-New York: Springer-Verlag. III, 160 p. DM 21.50; $ 12.70 (1980). ZBL0433.46049.