  We introduce a bilinear form for Weyl scalar perturbations of Kerr. The form
is symmetric and conserved, and we show that, when combined with a suitable
renormalization prescription involving complex r integration contours,
quasinormal modes are orthogonal in the bilinear form for different (l, m, n).
These properties are apparently not evident consequences of standard properties
for the radial and angular solutions to the decoupled Teukolsky relations and
rely on the Petrov type D character of Kerr and its t-$\phi$ reflection
isometry. We show that quasinormal mode excitation coefficients are given
precisely by the projection with respect to our bilinear form. These properties
can make our bilinear form useful to set up a framework for nonlinear
quasinormal mode coupling in Kerr. We also provide a general discussion on
conserved local currents and their associated local symmetry operators for
metric and Weyl perturbations, identifying a collection containing an
increasing number of derivatives.
