Jaffard families and localizations of star operations

We generalize the concept of localization of a star operation to flat overrings; subsequently, we investigate the possibility of representing the set Star(R) of star operations on R as the product of Star(T), as T ranges over a family of overrings of R with special properties. We then apply this method to study the set of star operations on a Prüfer domain R, in particular the set of stable star operations and the star-class groups of R