  We study D-branes in a two-dimensional Lorentzian orbifold R^{1,1}/\Gamma
with a discrete boost \Gamma. This space is known as Misner or Milne space, and
includes big crunch/big bang singularity. In this space, there are D0-branes in
spiral orbits and D1-branes with or without flux on them. In particular, we
observe imaginary parts of partition functions, and interpret them as the rates
of open string pair creation for D0-branes and emission of winding closed
strings for D1-branes. These phenomena occur due to the time-dependence of the
background. Open string 2 -> 2 scattering amplitude on a D1-brane is also
computed and found to be less singular than closed string case.
