Fix a variety X with a transitive (left) action by an algebraic
group G.  Let E and F be coherent sheaves on X. We prove that, for
elements g in a dense open subset of G, the sheaf Tor_i^X(E, g F)
vanishes for all i > 0.  When E and F are structure sheaves of
smooth subschemes of X in characteristic zero, this follows from
the Kleiman-Bertini theorem; our result has no smoothness
hypotheses or hypotheses on the characteristic of the ground field.