Let δ be a coaction of a locally compact group G on a C*-algebra A. We show that if I is a δ-invariant ideal in A, then 0 → I ×δI G → A ×δG → (A/I) ×δIG → 0 for full crossed products, as Landstad et al. have done for spatial crossed products by coactions. We prove that for suitable coactions, the crossed products of C0(X)-algebras are again C0(X)-algebras, and the crossed products of continuous C*-bundles by a locally compact group are again continuous C*-bundles.
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