  We consider a bounded domain $\Omega \subseteq \mathbb C^d$ which is a
$G$-space for a finite pseudoreflection group $G$. For each one-dimensional
representation of the group $G,$ the relative invariant subspace of the
weighted Bergman space on $\Omega$ is isometrically isomorphic to a weighted
Bergman space on the quotient domain $\Omega/G.$ Consequently, formulae
involving the weighted Bergman kernels and projections of $\Omega$ and $\Omega
/G$ are established. As a result, a transformation rule for the weighted
Bergman kernels under a proper holomorphic mapping with $G$ as its group of
deck transformations is obtained in terms of the character of the sign
representation of $G$. Explicit expressions for the weighted Bergman kernels of
several quotient domains (of the form $\Omega / G$) have been deduced to
demonstrate the merit of the described formulae.
