Exotic embeddings of smooth affine varieties

We find examples of exotic embeddings of smooth affine varieties into Cn in large codimensions. We show also examples of affine smooth, rational algebraic varieties X, for which there are algebraically exotic embeddings , which are holomorphically trivial. Using this we construct an infinite family {C2p+3} (p is a prime number) of complex manifolds, such that every C2p+3 has at least two different algebraic (quasi-affine) structures. We show also that there is a natural connection between Abhyankar–Sathaye Conjecture and the famous Quillen–Suslin Theorem.