2-cocycles and twisting of Kac algebras

We describe the twisting construction with the help of 2-cocycles on Hopfvon Neumann and George Kac algebras; we show that twisted Kac algebras are again Kac algebras. Using this construction, we give a wide class of new quantizations of the Heisenberg group and describe several series of non-trivial finite-dimensional C*-Hopf algebras (Kac algebras) of dimensions 4n and 2n(2) (n epsilon N) as twisting of finite groups.