  We discuss a quantum deformation of the Green-Schwarz superstring on flat
space, arising as a contraction limit of the corresponding deformation of AdS_5
x S^5. This contraction limit turns out to be equivalent to a previously
studied limit that yields the so-called mirror model - the model obtained from
the light cone gauge fixed AdS_5 x S^5 string by a double Wick rotation.
Reversing this logic, the AdS_5 x S^5 superstring is the double Wick rotation
of a quantum deformation of the flat space superstring. This quantum deformed
flat space string realizes symmetries of timelike kappa-Poincare type, and is T
dual to dS_5 x H^5, indicating interesting relations between symmetry algebras
under T duality. Our results directly extend to AdS_2 x S^2 x T^6 and AdS_3 x
S^3 x T^4, and beyond string theory to many (semi)symmetric space coset sigma
models, such as for example a deformation of the four dimensional Minkowski
sigma model with timelike kappa-Poincare symmetry. We also discuss possible
null and spacelike deformations.
