Basic gerbe over non-simply connected compact groups

We present an explicit construction of the basic bundle gerbes with connection over all connected compact simple Lie groups. These are geometric objects that appear naturally in the Lagrangian approach to the WZW conformal field theories. Our work extends the recent construction of Meinrenken The basic gerbe over a compact simple Lie group, L’Enseignement Mathematique, in press. arXiv:math. DG/0209194] restricted to the case of simply connected groups.