Modern discrete GPUs have been the processors of choice for accelerating compute-intensive applications, but using them in large-scale data processing is extremely challenging. Unfortunately, they do not provide important I/O abstractions long established in the CPU context, such as memory mapped files, which shield programmers from the complexity of buffer and I/O device management. However, implementing these abstractions on GPUs poses a problem: the limited GPU virtual memory system provides no address space management and page fault handling mechanisms to GPU developers, and does not allow modifications to memory mappings for running GPU programs. We implement ActivePointers, a software address translation layer and paging system that introduces native support for page faults and virtual address space management to GPU programs, and enables the implementation of fully functional memory mapped files on commodity GPUs. Files mapped into GPU memory are accessed using active pointers, which behave like regular pointers but access the GPU page cache under the hood, and trigger page faults which are handled on the GPU. We design and evaluate a number of novel mechanisms, including a translation cache in hardware registers and translation aggregation for deadlock-free page fault handling of threads in a single warp. We extensively evaluate ActivePointers on commodity NVIDIA GPUs using microbenchmarks, and also implement a complex image processing application that constructs a photo collage from a subset of 10 million images stored in a 40GB file. The GPU implementation maps the entire file into GPU memory and accesses it via active pointers. The use of active pointers adds only up to 1% to the application's runtime, while enabling speedups of up to 3.9x over a combined CPU+GPU implementation and 2.6x over a 12-core CPU-only implementation which uses AVX vector instructions.