On the interior motive of certain Shimura varieties: the case of Picard   surfaces
  The purpose of this article is to construct a Hecke-equivariant Chow motive whose realizations equal interior (or intersection) cohomology of Picard surfaces with regular algebraic coefficients. As a consequence, we are able to define Grothendieck motives for Picard modular forms. 
J. Wildeshaus
math.AG math.KT