  The recently published Kepler mission Data Release 25 (DR25) reported on
~197,000 targets observed during the mission. Despite this, no wide search for
red giants showing solar-like oscillations have been made across all stars
observed in Kepler's long-cadence mode. In this work, we perform this task
using custom apertures on the Kepler pixel files and detect oscillations in
21,914 stars, representing the largest sample of solar-like oscillating stars
to date. We measure their frequency at maximum power, $\nu_{\mathrm{max}}$,
down to $\nu_{\mathrm{max}}\simeq4\mu$Hz and obtain $\log(g)$ estimates with a
typical uncertainty below 0.05 dex, which is superior to typical measurements
from spectroscopy. Additionally, the $\nu_{\mathrm{max}}$ distribution of our
detections show good agreement with results from a simulated model of the Milky
Way, with a ratio of observed to predicted stars of 0.992 for stars with
10$\mu$Hz $ <\nu_{\mathrm{max}}<270\mu$Hz. Among our red giant detections, we
find 909 to be dwarf/subgiant stars whose flux signal is polluted by a
neighbouring giant as a result of using larger photometric apertures than those
used by the NASA Kepler Science Processing Pipeline. We further find that only
293 of the polluting giants are known Kepler targets. The remainder comprises
over 600 newly identified oscillating red giants, with many expected to belong
to the galactic halo, serendipitously falling within the Kepler pixel files of
targeted stars.
