  We study a polar tracer, having a concave surface, immersed in a
two-dimensional suspension of active particles. Using Brownian dynamics
simulations, we measure the distributions and auto-correlation functions of
forces and torque exerted by active particles on the tracer. The tracer
experiences a finite average force along its polar axis, while all the
correlation functions show exponential decay in time. Using these insights we
construct the full coarse-grained Langevin description for tracer position and
orientation, where the active particles are subsumed into an effective
self-propulsion force and exponentially correlated noise. The ensuing
mesoscopic dynamics can be described in terms of five dimensionless parameters.
We perform a thorough parameter study of the mean squared displacement, which
illustrates how the different parameters influence the tracer dynamics, which
crosses over from a ballistic to diffusive motion. We also demonstrate that the
distribution of tracer displacements evolves from a non-Gaussian shape at early
stages to a Gaussian behavior for sufficiently long times.
