Crossed product of \(C^{*}\)-algebras by hypergroups via group coactions (Q2883990)

The author constructs a type of crossed product out of a discrete group \(G\) which acts on a semi convo \(K\) and coacts on a \(C^{*}\)-algebra \(B\). The resulting algebra \(B\rtimes_{\delta ,\gamma}K\) can be regarded as a crossed product of \(B\) with a \(C^{*}\)-algebra which is constructed from the action of \(G\) on \(K\) in a previous paper by the author [Math. Slovaca 61, 645--652 (2011; Zbl 1265.46100)]) and is also motivated by the constructions given by \textit{A. an Huef} et al. [J. Pure Appl. Algebra 212, No. 10, 2344--2357 (2008; Zbl 1153.46043)]. The author gives a characterization of regular representations for such crossed products and obtains an imprimitivity theorem in the case where the chosen coaction of \(G\) in the construction is a dual coaction.