The C*-Algebra Generated by Operators with Compact Support on a Locally Compact Group

Let G be a locally compact group and VN(G) be the von Neumann algebra generated by the left regular representation of G. Let UCB(Ĝ) denote the C*-subalgebra generated by operators in VN(G) with compact support. When G is abelian, UCB(Ĝ) corresponds to the space of bounded uniformly continuous functions on the dual group Ĝ of G. In this paper we prove among other things that for a large class of locally compact groups which include the Heisenberg group, the "ax + b" group and the motion group, the centre of the Banach algebra UCB(Ĝ)* is the Fourier Stieltjes algebra B(G).