  For $G$ a finite group, a normalized 2-cocycle $\alpha\in
Z^{2}\big(G,{\mathbb S}^{1}\big)$ and $X$ a $G$-space on which a normal
subgroup $A$ acts trivially, we show that the $\alpha$-twisted $G$-equivariant
$K$-theory of $X$ decomposes as a direct sum of twisted equivariant
$K$-theories of $X$ parametrized by the orbits of an action of $G$ on the set
of irreducible $\alpha$-projective representations of $A$. This generalizes the
decomposition obtained in [G\'omez J.M., Uribe B., Internat. J. Math. 28
(2017), 1750016, 23 pages, arXiv:1604.01656] for equivariant $K$-theory. We
also explore some examples of this decomposition for the particular case of the
dihedral groups $D_{2n}$ with $n\ge 2$ an even integer.
