  A definition of a convolution of tensor fields on group manifolds is given,
which is then generalised to generic homogeneous spaces. This is applied to the
product of gauge fields in the context of `gravity $=$ gauge $\times$ gauge'.
In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST)
gauge transformations of two Yang-Mills gauge fields generate the linear BRST
diffeomorphism transformations of the graviton. This facilitates the definition
of the `gauge $\times$ gauge' convolution product on, for example, the static
Einstein universe, and more generally for ultrastatic spacetimes with compact
spatial slices.
