Abstract
In this paper, the braiding for a braided tensor category D is extended to a partially defined braiding on a non-braided tensor category C. C is constructed by considering a choice of left cosets representatives M for the action of a subgroup G of a finite group X on X. The objects of C are the right representations of G that graded by M. The group action and the grading in the definition of C were combined by considering a single object A spanned by a basis delta(S) circle times u for S is an element of M and u is an element of G. The double construction gives rise to a braided category D, the category of the representations of an algebra D which combines the actions and the gradings in the definition of D.