In in-memory database systems augmented by hardware accelerators, accelerating the index searching operations can greatly increase the runtime performance of database queries. Recently, adaptive radix trees (ART) have been shown to provide very fast index search implementation on the CPU. Here, we focus on an accelerator-based implementation of ART. We present a detailed performance study of our GPU-based adaptive radix tree (GRT) implementation over a variety of key distributions, synthetic benchmarks, and actual keys from music and book data sets. The performance is also compared with other index-searching schemes on the GPU. GRT on modern GPUs achieves some of the highest rates of index searches reported in the literature. For point queries, a throughput of up to 106 million and 130 million lookups per second is achieved for sparse and dense keys, respectively. For range queries, GRT yields 600 million and 1000 million lookups per second for sparse and dense keys, respectively, on a large dataset of 64 million 32-bit keys.