  Inspired by the covering-space method in path integral on multiply connected
spaces, we here present a universal formula of time-evolution kernels for
continuous- and discrete-time quantum walks on orbit spaces. In this note, we
focus on the case in which walkers' configuration space is the orbit space
$\Lambda/\Gamma$, where $\Lambda$ is an arbitrary lattice and $\Gamma$ is a
discrete group whose action on $\Lambda$ has no fixed points. We show that the
time-evolution kernel on $\Lambda/\Gamma$ can be written as a weighted sum of
time-evolution kernels on $\Lambda$, where the summation is over the orbit of
initial point in $\Lambda$ and weight factors are given by a one-dimensional
unitary representation of $\Gamma$. Focusing on one dimension, we present a
number of examples of the formula. We also present universal formulas of
resolvent kernels, canonical density matrices, and unitary representations of
arbitrary groups in quantum walks on $\Lambda/\Gamma$, all of which are
constructed in exactly the same way as for the time-evolution kernel.
