  The cancellation problem asks if two complex algebraic varieties X and Y of
the same dimension such that X\times\mathbb{C} and Y\times\mathbb{C} are
isomorphic are isomorphic. Iitaka and Fujita established that the answer is
positive for a large class of varieties of any dimension. In 1989, Danielewski
constructed a famous counter-example using smooth affine surfaces with additive
group actions. His construction was further generalized by Fieseler and Wilkens
to describe a larger class of affine surfaces. Here we construct higher
dimensional analogues of these surfaces. We study algebraic actions of the
additive group \mathbb{C}\_{+} on certain of these varieties, and we obtain
counter-examples to the cancellation problem in any dimension n\geq2 .
