  Recently Francisco Presas Mata constructed the first examples of closed
contact manifolds of dimension larger than 3 that contain a plastikstufe, and
hence are non-fillable. Using contact surgery on his examples we create on
every sphere S^{2n-1}, n>1, an exotic contact structure \xi_- that also
contains a plastikstufe. As a consequence, every closed contact manifold M
(except S^1) can be converted into a contact manifold that is not
(semi-positively) fillable by taking the connected sum of M with
(S^{2n-1},\xi_-).
