We prove that certain algebra quotients of Hopf algebras are twisted Hopf algebras. On the other handuq(sl(2)) is a crossed product of a central subalgebra with a quotient Ʉ, whenqis a root of 1. Using the cocycle involved in this crossed product we construct non-trivial complex cocycles τ and we find the isomorphism classes of the corresponding twisted Hopf algebrasτɄ. These provide complex projective representations of Ʉ which are not ordinary representations.