  We present time-series VI photometry of the metal-rich ([Fe/H] = -0.53)
globular cluster NGC 6441. Our color-magnitude diagram shows that the extended
blue horizontal branch seen in Hubble Space Telescope data exists in the
outermost reaches of the cluster. The red clump slopes nearly parallel to the
reddening vector. A component of this slope is due to differential reddening,
but part is intrinsic. The blue horizontal branch stars are more centrally
concentrated than the red clump stars. We have discovered about 50 new variable
stars near NGC 6441, among them eight or more RR Lyrae stars which are very
probably cluster members. Comprehensive period searches over the range 0.2-1.0
days yielded unusually long periods (0.5-0.9 days) for the fundamental
pulsators compared with field RR Lyrae of the same metallicity. Three similar
long-period RR Lyrae are known in other metal-rich globulars. With over ten
examples in hand, it seems that a distinct sub-class of RR Lyrae is emerging.
The observed properties of the horizontal branch stars are in reasonable
agreement with recent models which invoke deep mixing to enhance the
atmospheric helium abundance, while they conflict with models which assume high
initial helium abundance. The light curves of the c-type RR Lyrae seem to have
unusually long rise times and sharp minima. Reproducing these light curves in
stellar pulsation models may provide another means of constraining the physical
variables responsible for the anomalous blue horizontal branch extension and
sloped red clump observed in NGC 6441.
