  AIMS: We investigated the optical variability of the symbiotic binary FN Sgr,
with photometric monitoring during $\simeq$55 years and with a high-cadence
Kepler light curve lasting 81 days. METHODS: The data obtained in the V and I
bands were reduced with standard photometric methods. The Kepler data were
divided into subsamples and analyses with the Lomb-Scargle algorithm. RESULTS:
The V and I band light curves showed a phenomenon never before observed with
such recurrence in any symbiotic system, namely short outbursts, starting
between orbital phase 0.3 and 0.5 and lasting about a month, with a fast rise
and a slower decline, and amplitude of 0.5-1 mag. In the Kepler light curve we
discovered three frequencies with sidebands. We attribute a stable frequency of
127.5 d$^{-1}$ (corresponding to an 11.3 minutes period) to the white dwarf
rotation. We suggest that this detection probably implies that the white dwarf
accretes through a magnetic stream, like in intermediate polars. The small
outbursts may be ascribed to the stream-disc interaction. Another possibility
is that they are due to localized thermonuclear burning, perhaps confined by
the magnetic field, like recently inferred in intermediate polars, albeit on
different timescales. We measured also a second frequency around 116.9 d$^{-1}$
(corresponding to about 137 minutes), which is much less stable and has a
drift. It may be due to rocky detritus around the white dwarf, but it is more
likely to be caused by an inhomogeneity in the accretion disk. Finally, there
is a third frequency close to the first one that appears to correspond to the
beating between the rotation and the second frequency.
