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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.

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    $\begingroup$ Example 4.4.7 in Rordam's text Classification of Nuclear Simple C*-algebras contains a description of $\mathcal{O}_2$ as a crossed product of continuous functions on a Cantor set by $\mathbb{Z}_2*\mathbb{Z}_3.$ $\endgroup$
    – Caleb Eckhardt
    Commented Jul 19, 2023 at 15:28

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