The main result of this paper establishes an explicit ring isomorphism between the twisted orbifold K-theory ω K orb ([ * / G]) and R( D ω (G)) for any element ω ∈ Z 3 (G; S 1 ).We also study the relation between the twisted orbifold K-theories α K orb (ᐄ)where G and G are different finite groups, and α ∈ Z 3 (G; S 1 ) and α ∈ Z 3 (G ; S 1 ) are different twistings.We prove that if G is an extraspecial group with prime number p as an index and order p n (for some fixed n ∈ ‫,)ގ‬ under a suitable hypothesis over the twisting α we can obtain a twisting α on the group ‫ޚ(‬ p ) n such that there exists an isomorphism between the twisted K-theories α K orb ([ * / G ]) and α K orb ‫ޚ(/ * [(‬ p ) n ]).