Abstract
Suppose that
G
has a representation group
H
, that
G
ab
:=G/
[G,G]
¯
is compactly generated, and that
A
is a \cs-algebra for which the complete regularization of $\Prim(A)$ is a locally compact Hausdorff space
X
. In a previous article, we showed that there is a bijection
α↦(
Z
α
,
f
α
)
between the collection of exterior equivalence classes of locally inner actions $\alpha:G\to\Aut(A)$, and the collection of principal $\hgab$-bundles
Z
α
together with continuous functions $f_\alpha:X\to H^2(G,\T)$. In this paper, we compute the crossed products
A
⋊
α
G
in terms of the data
Z
α
,
f
α
, and~$\cs(H)$.