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\section{Outline}  In this paper we demonstrate how the photo-dressing of electrons in a solid leads to a rich non-equilibrium bandstructure and how the formation of quasiparticle bands of the combined photon-electron states can be directly observed in td-ARPES measurements.  We simulate the pump-probe photoemission process and angle reosolved measurement, as depicted in Fig.~1a, where the pump is a circularly polarized monochromatic pulse that is long enough to drive the electronic structure into a non-equilibrium but stationary state. The probe is typically much shorter but with a higher energy, large enough to ionize electrons from the sample (HH: here a bit more on how photoemission gives the electronic structure). The atomic structure of monolayer WSe$_2$, which crystalises in with hexagonal symmetry, is depicted in Fig.~1b, along with the Brillouin zone and the path across the $K$ point that we are considering here. The observed photoelectron spectrum depends strongly on the overlap of the pump and probe pulses as shown in Fig.~1d. When the two pulses do not overlap one only measures the equilibrium bandstructure of WSe2, but in case of overlapping pulses extra features occur in the spectrum. The non-equilibrium state of the driven monolayer consists of quasiparticles that are a combination of electrons from the material and photons from the driving field, so called photon-dressed electronic states.  1. Our calculations show that depending on the delay between pump and probe lasers Floquet bands appear in the photo electron spectrum at energies controlled by the parameters of the pump pulse. By simulating a slow switching off process, we show how these Floquet bands collapse and finally combine with the equilibrium bands.   Fig. 1 "movie" (including pump-probe overlap cartoons)