  We consider the operator product expansion for quantum field theories on
general analytic 4-dimensional curved spacetimes within an axiomatic framework.
We prove under certain general, model-independent assumptions that such an
expansion necessarily has to be invariant under a simultaneous reversal of
parity, time, and charge (PCT) in the following sense: The coefficients in the
expansion of a product of fields on a curved spacetime with a given choice of
time and space orientation are equal (modulo complex conjugation) to the
coefficients for the product of the corresponding charge conjugate fields on
the spacetime with the opposite time and space orientation. We propose that
this result should be viewed as a replacement of the usual PCT theorem in
Minkowski spacetime, at least in as far as the algebraic structure of the
quantum fields at short distances is concerned.
