  Investigations of the origin and evolution of the Milky Way disk have long
relied on chemical and kinematic identification of its components to
reconstruct our Galactic past. Difficulties in determining precise stellar ages
have restricted most studies to small samples, normally confined to the solar
neighbourhood. Here we break this impasse with the help of asteroseismic
inference and perform a chronology of the evolution of the disk throughout the
age of the Galaxy. We chemically dissect the Milky Way disk population using a
sample of red giant stars spanning out to 2~kpc in the solar annulus observed
by the {\it Kepler} satellite, with the added dimension of asteroseismic ages.
Our results reveal a clear difference in age between the low- and high-$\alpha$
populations, which also show distinct velocity dispersions in the $V$ and $W$
components. We find no tight correlation between age and metallicity nor
[$\alpha$/Fe] for the high-$\alpha$ disk stars. Our results indicate that this
component formed over a period of more than 2~Gyr with a wide range of [M/H]
and [$\alpha$/Fe] independent of time. Our findings show that the kinematic
properties of young $\alpha$-rich stars are consistent with the rest of the
high-$\alpha$ population and different from the low-$\alpha$ stars of similar
age, rendering support to their origin being old stars that went through a mass
transfer or stellar merger event, making them appear younger, instead of
migration of truly young stars formed close to the Galactic bar.
