  One of the most difficult properties to derive for stars is their age. For
cool main-sequence stars, gyrochronology relations can be used to infer stellar
ages from measured rotation pe- riods and HR Diagram positions. These relations
have few calibrators with known ages for old, long rotation period stars. There
is a significant sample of old Kepler objects of inter- est, or KOIs, which
have both measurable surface rotation periods and precise asteroseismic
measurements from which ages can be accurately derived. In this work we
determine the age and the rotation period of solar-like pulsating KOIs to both
compare the rotation properties of stars with and without known planets and
enlarge the gyrochronology calibration sample for old stars. We use Kepler
photometric light curves to derive the stellar surface rotation peri- ods while
ages are obtained with asteroseismology using the Asteroseismic Modeling Portal
in which individual mode frequencies are combined with high-resolution
spectroscopic pa- rameters. We thus determine surface rotation periods and ages
for 11 planet-hosting stars, all over 2 Gyr old. We find that the
planet-hosting stars exhibit a rotational behaviour that is consistent with the
latest age-rotation models and similar to the rotational behaviour of stars
without detected planets. We conclude that these old KOIs can be used to test
and calibrate gyrochronology along with stars not known to host planets.
