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Kinetic plasma simulations using an electromagnetic particle-in-cell (PIC) algorithm have become the tool of choice for numerical modeling of several astrophysical and laboratory scenarios, ranging from astrophysical shocks and plasma shell collisions, to high-intensity laser-plasma interactions, with applications to fast ignition and particle acceleration. However, fully relativistic kinetic codes are computationally intensive, and new computing paradigms are required for one-to-one direct modeling of these scenarios. In this paper, we look at the use of modern graphics processing units for PIC algorithm calculations, discussing the implementation of a fully relativistic PIC code using NVIDIA's Compute Unified Device Architecture, also allowing one for simultaneous visualization of simulation results with negligible impact on performance. Details on the algorithm implementation are given, focusing on grid-particle interpolation and current deposition and also on the direct visualization routines. Finally, we present results from a test simulation of an electron/positron plasma shell collision, focusing on code validation and performance evaluation.