Reduction of strongly equivariant bundle gerbes with connection and curving

From a certain strongly equivariant bundle gerbe with connection and curving over a smooth manifold on which a Lie group acts, we construct under some conditions a bundle gerbe with connection and curving over the quotient space. In general, the construction requires a choice, and we can consequently obtain distinct stable isomorphism classes of bundle gerbes with connection and curving over the quotient space. A bundle gerbe naturally arising in Chern-Simons theory provides an example of the reduction.