  There has been a long-standing debate on the coexistence between itinerant
electrons and localized spins in the PdCrO$_2$ delafossite. By means of the
charge self-consistent combination of density functional theory and dynamical
mean-field theory, it is corroborated that despite overall remarkable metallic
response, the CrO$_2$ layers are indeed Mott insulating as suggested by
previous experimental work. The resulting ${\bf k}$-resolved spectral function
in the paramagnetic phase is in excellent agreement with available
photoemission data. Subtle coupling between the itinerant and Mott-localized
degrees of freedom is revealed. Different doping scenarios are simulated in
order to manipulate the electronic states within the inert layers. In
particular, oxygen vacancies prove effective in turning the hidden Mott
insulator into a strongly correlated itinerant subsystem. The present results
may open a new venue in research on quantum materials beyond canonical
classification schemes.
