Multiple displays are commonly used in meetings and discussion rooms. These settings provide new challenges for designing fluid interaction across displays. For instance, a list of primitive interaction tasks in such environments has not been investigated in literature. In addition, past researchers have carried out their research using mobile phones as input devices to control displays. However, it is still unclear whether an input device with an integrated display can improve the performance of multi-display interaction tasks. This research contributes to the design space of the multi-display environments (MDE) in two aspects. Its first contribution is theoretical, as it lists the primitive interaction tasks for MDEs. This list helps interaction designers, who design new input devices, to be aware of the tasks that the device should support. Furthermore, it can be used as criteria to evaluate novel input devices. The second contribution of this research is practical and it is aimed at answering the following research question: Does a mobile input device with an integrated display improve performing cross-display interaction tasks?