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K2 was a community-driven NASA mission where all targets were proposed through guest observer programs. Among those, the K2 Galactic Archaeology Program (K2GAP) was devoted to measuring asteroseismic signals from giant stars to inform studies of the Galaxy, with about 25% of the observed K2 targets being allocated to this program. Here, we provide an overview of this program. We discuss in detail the target selection procedure and provide a python code that implements the selection function, see this https URL . Additionally, we discuss the detection completeness of the asteroseismic parameters $\nu_{\rm max}$ and $\Delta \nu$. Broadly speaking, the targets were selected based on 2MASS color $J-Ks > 0.5$, with finely tuned adjustments for each campaign. Making use of the selection function we compare the observed distribution of asteroseismic masses to theoretical predictions. The median asteroseismic mass is higher by about 4% compared to predictions. Additionally, the number of seismic detections is on average 14% lower than expected. We provide a selection-function-matched mock catalog of stars based on a synthetic model of the Galaxy for the community to be used in subsequent analyses of the K2GAP data set, see this http URL .