  The long-term monitoring and high photometric precision of the Kepler
satellite will provide a unique opportunity to sound the stellar cycles of many
solar-type stars using asteroseismology. This can be achieved by studying
periodic changes in the amplitudes and frequencies of the oscillation modes
observed in these stars. By comparing these measurements with conventional
ground-based chromospheric activity indices, we can improve our understanding
of the relationship between chromospheric changes and those taking place deep
in the interior throughout the stellar activity cycle. In addition,
asteroseismic measurements of the convection zone depth and differential
rotation may help us determine whether stellar cycles are driven at the top or
at the base of the convection zone. In this paper, we analyze the precision
that will be possible using Kepler to measure stellar cycles, convection zone
depths, and differential rotation. Based on this analysis, we describe a
strategy for selecting specific targets to be observed by the Kepler
Asteroseismic Investigation for the full length of the mission, to optimize
their suitability for probing stellar cycles in a wide variety of solar-type
stars.
