Isotropy fibers of ideals in groupoid C${}^{\ast }$-algebras

Given a locally compact étale groupoid and an ideal $I$ in its groupoid C${}^{\ast }$-algebra, we show that $I$ defines a family of ideals in group C${}^{\ast }$-algebras of the isotropy groups and then study to which extent $I$ is determined by this family. As an application we obtain the following results: (a) prove that every proper ideal is contained in an induced primitive ideal; (b) describe the maximal ideals; © classify the primitive ideals for a class of graded groupoids with essentially central isotropy.