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For a C*-algebra A with an action of a locally compact abelian group G, one considers the pure states of A with the associated action. Type I orbits are defined and studied in the previous paper [4]. We continue this study; in particular, we shall show that if A is separable and simple and if there is a type I orbit through a pure state / with trivial stabilizer {t^G: 7r/°o:j~~/} = {0}, then there is a type I orbit with stabilizer equal to any given closed subgroup of G.

Type {${\rm I}$} orbits in the pure states of a {$C\sp \ast$}-dynamical system