  Time series observations of a single dithered field centered on the diffuse
dwarf satellite galaxy Crater II were obtained with the Dark Energy Camera
(DECam) at the 4m Blanco Telescope at Cerro Tololo Inter-American Observatory,
Chile, uniformly covering up to two half-light radii. Analysis of the $g$ and
$i$ time series results in the identification and characterization of 130
periodic variable stars, including 98 RR Lyrae stars, 7 anomalous Cepheids, and
1 SX Phoenicis star belonging to the Crater II population, and 24 foreground
variables of different types. Using the large number of ab-type RR Lyrae stars
present in the galaxy, we obtained a distance modulus to Crater II of
$(m-M)_0=20.333\pm 0.004$ (stat) $\pm 0.07$ (sys). The distribution of the RR
Lyrae stars suggests an elliptical shape for Crater II, with an ellipticity of
0.24 and a position angle of $153^\circ$. From the RR Lyrae stars we infer a
small metallicity dispersion for the old population of Crater II of only 0.17
dex. There are hints that the most metal-poor stars in that narrow distribution
have a wider distribution across the galaxy, while the slightly more metal rich
part of the population is more centrally concentrated. Given the features in
the color-magnitude diagram of Crater II, the anomalous Cepheids in this galaxy
must have formed through a binary evolution channel of an old population.

Astrophysics of Galaxies;Solar and Stellar Astrophysics