  If C is a stable model category with a monoidal product then the set of
homotopy classes of self-maps of the unit S forms a commutative ring. An
idempotent e of this ring will split the homotopy category. We prove that
provided the localised model structures exist, this splitting of the homotopy
category comes from a splitting of the model category, that is, C is Quillen
equivalent to the product of C localised at the object eS and C localised at
the object (1-e)S. This Quillen equivalence is strong monoidal and is symmetric
when the monoidal product of C is.
