  The spectral function of a spin-balanced two-dimensional Fermi gas with
short-range interactions is calculated by means of a quantum cluster expansion.
Good qualitative agreement is found with a recent experiment by Feld
$\textit{et al.}$ [Nature (London) $\textbf{480}$, 75 (2011)]. The effects of
pairing are clearly visible in the density of states, which displays a
suppression of spectral weight due to the formation of a two-body bound state.
In addition, the momentum distribution and the radio-frequency spectrum are
derived, which are in excellent agreement with exact universal results. It is
demonstrated that in the limit of high temperature, the quasiparticle
excitations are well defined, allowing for a kinetic description of the gas.
