Algebraic Structures Associated to Orbifold Wreath Products

We present structure theorems in terms of inertial decompositions for the wreath product ring of an orbifold presented as the quotient of a smooth, closed manifold by a compact, connected Lie group acting almost freely. In particular we show that this ring admits lambda-ring and Hopf algebra structures both abstractly and directly. This generalizes results known for global quotient orbifolds by finite groups.