  We study the synchronization of a linear array of globally coupled identical
logistic maps. We consider a time-delayed coupling that takes into account the
finite velocity of propagation of the interactions. We find globally
synchronized states in which the elements of the array evolve along a periodic
orbit of the uncoupled map, while the spatial correlation along the array is
such that an individual map sees all other maps in his present, current, state.
For values of the nonlinear parameter such that the uncoupled maps are chaotic,
time-delayed mutual coupling suppress the chaotic behavior by stabilizing a
periodic orbit which is unstable for the uncoupled maps. The stability analysis
of the synchronized state allows us to calculate the range of the coupling
strength in which global synchronization can be obtained.
