Double group construction of quantum groups in the von Neumann algebra framework

We introduce a notion of double group construction within the category of q uasi Woronowicz algebras which are regarded as quantum groups in the von Ne umann algebra framework. We show that the quantum double in this setting is always unimodular. The Kac-Takesaki operator of the double group is explic itly described. It is also proven that the dual of the quantum double has a quasitriangular structure.