The stellar populations in the inner kiloparsecs of the Milky Way (MW) show complex kinematical and chemical structures. The origin and evolution of these structures is still under debate. Here we study the central region of a fully cosmological hydrodynamical simulation of a disk galaxy that reproduces key properties of the inner kiloparsecs of the MW: it has a boxy morphology and shows an overall rotation and dispersion profile in agreement with observations. We use a clustering algorithm on stellar kinematics to identify a number of discrete kinematic components: a high- and low-spin disk, a stellar halo and two bulge components; one fast rotating and one slow-rotating. We focus on the two bulge components and show that the slow rotating one is spherically symmetric while the fast rotating component shows a boxy/peanut morphology. Although the two bulge components are kinematically discrete populations at present-day, they are both mostly formed over similar time scales, from disk material. We find that stellar particles with lower initial birth angular momentum (most likely thick disc stars) end up in the slow-rotating low-spin bulge, while stars with higher birth angular momentum (most likely thin disc stars) are found in the high-spin bulge. This has the important consequence that a bulge population with a spheroidal morphology does not necessarily indicate a merger origin. In fact, we do find that only $sim2.3$% of the stars in the bulge components are ex-situ stars brought in by accreted dwarf galaxies early on. We identify these ex-situ stars as the oldest and most metal-poor stars on highly radial orbits with large vertical excursions from the disk.
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