  We study the motivic cohomology of the special fiber of quaternionic Shimura
varieties at a prime of good reduction. We exhibit classes in these motivic
cohomology groups and use this to give an explicit geometric realization of
level raising between Hilbert modular forms. The main ingredient for our
construction is a form of Ihara's Lemma for compact quaternionic Shimura
surfaces which we prove by generalizing a method of Diamond-Taylor. Along the
way we also verify the Hecke orbit conjecture for these quaternionic Shimura
varieties which is a key input for our proof of Ihara's Lemma.
