The application resource specification--a static specification of several parameters such as the number of threads and the scratchpad memory usage per thread block--forms a critical component of the existing GPU programming models. This specification determines the performance of the application during execution because the corresponding on-chip hardware resources are allocated and managed purely based on this specification. This tight coupling between the software-provided resource specification and resource management in hardware leads to significant challenges in programming ease, portability, and performance, as we demonstrate in this work. Our goal in this work is to reduce the dependence of performance on the software-provided resource specification to simultaneously alleviate the above challenges. To this end, we introduce Zorua, a new resource virtualization framework, that decouples the programmer-specified resource usage of a GPU application from the actual allocation in the on-chip hardware resources. Zorua enables this decoupling by virtualizing each resource transparently to the programmer. We demonstrate that by providing the illusion of more resources than physically available, Zorua offers several important benefits: (i) Programming Ease: Zorua eases the burden on the programmer to provide code that is tuned to efficiently utilize the physically available on-chip resources. (ii) Portability: Zorua alleviates the necessity of re-tuning an application's resource usage when porting the application across GPU generations. (iii) Performance: By dynamically allocating resources and carefully oversubscribing them when necessary, Zorua improves or retains the performance of applications that are already highly tuned to best utilize the resources. The holistic virtualization provided by Zorua has many other potential uses which we describe in this paper.