  We put the known results on the antipode of a usual quasitriangular Hopf
algebra into the framework of multiplier Hopf algebras. We illustrate with
examples which can not be obtained using classical Hopf Algebras. The focus of
the present paper lies on the class of the so-called group cograded multiplier
Hopf algebras. By doing so, we bring the results of quasitriangular Hopf
group-coalgebras (as introduced by Turaev) to the more general framework of
multiplier Hopf algebras.
