Decomposition of bent generalized Boolean functions

A one to one correspondence between regular generalized bent functions from $\F_2^n$ to $\Z_{2^m},$ and $m-$tuples of Boolean bent functions is established. This correspondence maps self-dual (resp. anti-self-dual) generalized bent functions to $m-$tuples of self-dual (resp. anti self-dual) Boolean bent functions. An application to the classification of regular generalized bent functions under the extended affine group is given.