Full crossed products by coactions, C-0(X)-algebras and C*-bundles

Let delta be a coaction of a locally compact group G on a C*-algebra A. We show that if I is a delta-invariant ideal in A, then 0 --> I x (delta I) G --> A x(delta) G --> (A/I) x (delta I)G --> 0 for full crossed products, as Landstad et al, have done for spatial crossed products by coactions. We pr ove that for suitable coactions, the crossed products of C-0(X)-algebras ar e again C-0(X)-algebras, and the crossed products of continuous C*-bundles by a locally compact group are again continuous C*-bundles.