  We consider a $R^{1,d}/Z_2$ orbifold, where $Z_2$ acts by time and space
reversal, also known as the embedding space of the elliptic de Sitter space.
The background has two potentially dangerous problems: time-nonorientability
and the existence of closed time-like curves. We first show that closed causal
curves disappear after a proper definition of the time function. We then
consider the one-loop vacuum expectation value of the stress tensor. A naive
QFT analysis yields a divergent result. We then analyze the stress tensor in
bosonic string theory, and find the same result as if the target space would be
just the Minkowski space $R^{1,d}$, suggesting a zero result for the
superstring. This leads us to propose a proper reformulation of QFT, and
recalculate the stress tensor. We find almost the same result as in Minkowski
space, except for a potential divergence at the initial time slice of the
orbifold, analogous to a spacelike Big Bang singularity. Finally, we argue that
it is possible to define local S-matrices, even if the spacetime is globally
time-nonorientable.
