  Coactions of Hopf C*-bimodules simultaneously generalize coactions of Hopf
C*-algebras and actions of groupoids. Following an approach of Baaj and
Skandalis, we construct reduced crossed products and establish a duality for
fine coactions. Examples of coactions arise from Fell bundles on groupoids and
actions of a groupoid on bundles of C*-algebras. Continuous Fell bundles on an
etale groupoid correspond to coactions of the reduced groupoid algebra, and
actions of a groupoid on a continuous bundle of C*-algebras correspond to
coactions of the function algebra.

Operator Algebras;Quantum Algebra