On twisted ordered monoid rings over quasi-Baer rings

In this paper we show that if M is an Ordered monoid then the twisted monoid ring R^T M is (left principally) quasi-Baer if and only if R is (left principally) quasi-Baer. Also if R is (left principally) quasi-Baer and G is an ordered group acting on R we give a necessary and sufficient condition for the crossed product R G to be (left principally) quasi-Baer.