Subalgebras generated by extreme points in Fourier-Stieltjes algebras of locally compact groups

Let G be a locally compact group, G* be the set of all extreme points of the set of normalized continuous positive definite functions of G, and a(G) be the closed subalgebra generated by G* in B(G). When G is abelian, G* is the set of Dirac measures of the dual group (G) over cap, and a(G) can be identified as l(1)(G) over cap. We study the properties of a(G), particularly its spectrum and its dual von Neumann algebra.