An analytical study is presented for the quasisteady translation and steady rotation of a spherical particle covered by a layer of adsorbed polymers located at the center of a spherical cavity that may also have an adsorbed polymer layer on its inside wall. The Reynolds number is assumed to be small, and the surface polymer layers are assumed to be thin with respect to the particle radius and the spacing between solid surfaces. To solve the Stokes flow equations within and outside the polymer layers a method of matched asymptotic expansions in small parameters lambda(1) and lambda(2) is used, where lambda(1) and lambda(2) are the ratios of the polymer-layer length scale to the radius of curvature at the particle surface and at the cavity wall, respectively. The results for the hydrodynamic force and torque exerted on the particle are expressed as an effective hydrodynamic thickness (L) of the adsorbed polymer layer surrounding the particle, which are accurate to O(lambda(1)(2)). The O(lambda(1)) term for L normalized by its value in the absence of the cavity is found to be independent of the polymer segment distribution, the hydrodynamic interactions among the segments, and the volume fraction of the segments. The O(lambda(1)(2)) term for L, however, is a sensitive function of the polymer segment distribution and the volume fraction of the segments. In general, the boundary effects on the motion of a polymer-coated particle can be quite significant in appropriate situations.