  This paper exposes the fundamental role that the Drinfel'd double $\dkg$ of
the group ring of a finite group $G$ and its twists $\dbkg$, $\beta \in
Z^3(G,\uk)$ as defined by Dijkgraaf--Pasquier--Roche play in stringy orbifold
theories and their twistings.
  The results pertain to three different aspects of the theory. First, we show
that $G$--Frobenius algebras arising in global orbifold cohomology or K-theory
are most naturally defined as elements in the braided category of
$\dkg$--modules. Secondly, we obtain a geometric realization of the Drinfel'd
double as the global orbifold $K$--theory of global quotient given by the
inertia variety of a point with a $G$ action on the one hand and more
stunningly a geometric realization of its representation ring in the braided
category sense as the full $K$--theory of the stack $[pt/G]$. Finally, we show
how one can use the co-cycles $\beta$ above to twist a) the global orbifold
$K$--theory of the inertia of a global quotient and more importantly b) the
stacky $K$--theory of a global quotient $[X/G]$. This corresponds to twistings
with a special type of 2--gerbe.
