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

Additive group actions on Danielewski varieties and the cancellation problem