Summary: Actions and coactions of finite

${C}^{*}$-quantum groupoids are studied in an operator algebras context. In particular, we prove a double crossed product theorem, and the existence of a universal von Neumann algebra on which any finite groupoid acts outerly. We give two actually different extensions of the matched pairs procedure. In [Publ. Mat. Urug. 10, 11–51 (2005;

Zbl 1092.16021)],

*N. Andruskiewitsch* and

*S. Natale* defined, for any matched pair of groupoids, two

${C}^{*}$-quantum groupoids in duality; we give here an interpretation of them in terms of crossed products of groupoids using a single multiplicative partial isometry which gives a complete description of these structures. The second extension deals only with groups to define another type of finite

${C}^{*}$-quantum groupoids.