We model the transport of a microscopic particle via a regular array of beating elastic cilia, whose tips experience an adhesive interaction with the particle's surface. At optimal adhesion strength, the average particle velocity is maximized. Using simulations spanning a range of cilia stiffness and cilia-particle adhesion strength, we explore the parameter space over which the particle can be "released", "propelled", or "trapped" by the cilia. We use a lower-order model to predict parameters for which the cilia are able to "propel" the particle. This is the first study that shows how both stiffness and adhesion strength are crucial for manipulation of particles by active cilia arrays. These results can facilitate the design of synthetic cilia that integrate adhesive and hydrodynamic interactions to selectively repel or trap particulates. Surfaces that are effective at repelling particulates are valuable for antifouling applications, while surfaces that can trap and, thus, remove particulates from the solution are useful for efficient filtration systems.