This paper presents results of the resolved simulation of particles suspended in a fluid in shear flow. Unlike most of the existing work on this subject, the ratio of the particle density to that of the suspending fluid is not 1 but varies between 2.5 and 10, with a focus on inertial effects rather than gravity, which is not considered. Two particle Reynolds numbers are considered, 20 and 40, while the average particle volume fraction varies from 5% to 33%. The study focuses on the effects of inertia on this class of flows. It is shown that the memory of the particles' earlier state of motion associated with inertia is responsible for significant effects. Among others, the collision rate is increased and, with it, the rate of momentum transfer from the moving walls into the bulk of the fluid-particle mixture; normal stress differences become larger and the particle-rich layer near the walls becomes denser. Comparable effects are found by increasing the particle density and the particle Reynolds number. The two normal stress differences are found to be both negative and comparable in spite of their very different physical origin. Additional results concern the wall slip, the stresslet, the effects of a nonzero collisional tangential force, the wall stress, and others. The great importance of particle-particle and particle-wall collisions reveals itself in influencing the rheology of the mixture, the normal stress differences, and the transport of momentum.