  We investigate both geometric and conformal field theoretic aspects of mirror
symmetry on N=(4,4) superconformal field theories with central charge c=6. Our
approach enables us to determine the action of mirror symmetry on (non-stable)
singular fibers in elliptic fibrations of Z_N orbifold limits of K3. The
resulting map gives an automorphism of order 4,8, or 12, respectively, on the
smooth universal cover of the moduli space. We explicitly derive the geometric
counterparts of the twist fields in our orbifold conformal field theories. The
classical McKay correspondence allows for a natural interpretation of our
results.
