  In the search for physics beyond the Standard Model the Mu3e experiment tries
to observe the lepton flavor violating decay $\mu^+ \rightarrow e^+ e^- e^+$.
By observing the decay products of $1 \cdot 10^8\mu$/s it aims to either
observe the process, or set a new upper limit on its estimated branching ratio.
The high muon rates result in high data rates of $80$\,Gbps, dominated by data
produced through background processes. We present the Online Event Selection, a
three step algorithm running on the graphics processing units (GPU) of the $12$
Mu3e filter farm computers.
  By using simple and fast geometric selection criteria, the algorithm first
reduces the amount of possible event candidates to below $5\%$ of the initial
set. These candidates are then used to reconstruct full particle tracks,
correctly reconstructing over $97\%$ of signal tracks. Finally a possible decay
vertex is reconstructed using simple geometric considerations instead of a full
reconstruction, correctly identifying over $94\%$ of signal events.
  We also present a full implementation of the algorithm, fulfilling all
performance requirements at the targeted muon rate and successfully reducing
the data rate by a factor of $200$.
