  We demonstrate the existence of an exact invariant solution to the
Navier-Stokes equations for the asymptotic suction boundary layer. The
identified periodic orbit with a very long period of several thousand advective
time units is found as a local dynamical attractor embedded in the stability
boundary between laminar and turbulent dynamics. Its dynamics captures both the
interplay of downstream oriented vortex pairs and streaks observed in numerous
shear flows as well as the energetic bursting that is characteristic for
boundary layers. By embedding the flow into a family of flows that interpolates
between plane Couette flow and the boundary layer we demonstrate that the
periodic orbit emerges in a saddle-node infinite-period (SNIPER) bifurcation of
two symmetry-related travelling wave solutions of plane Couette flow.
Physically, the long period is due to a slow streak instability which leads to
a violent breakup of a streak associated with the bursting and the reformation
of the streak at a different spanwise location. We show that the orbit is
structurally stable when varying both the Reynolds number and the domain size.
