Suppose that (G, T) is a second countable locally compact transformati
on group given by a homomorphism l: G --> Homeo(T), and that A is a se
parable continuous-trace C-algebra with spectrum T. An action alpha:
G --> Aut(A) is said to cover l if the induced action of G on T coinci
des with the original one. We prove that the set Br,(T) of Morita equi
valence classes of such systems forms a group with multiplication give
n by the balanced tensor product: [A, alpha][B, beta] = [A x C-0(T), B
, alpha x beta], and we refer to Br-G(T) as the Equivariant Brauer Gro
up. We give a detailed analysis of the structure of Br-G(T) in terms o
f the Moore cohomology of the group G and the integral cohomology of t
he space T. Using this, we can characterize the stable continuous-trac
e C-algebras with spectrum T which admit actions covering l. In parti
cular, we prove that if G = R, then every stable continuous-trace C-a
lgebra admits an (essentially unique) action covering l, thereby subst
antially improving results of Raeburn and Rosenberg. (C) 1997 Academic
Press.