We present a new scalable, lightweight algorithm to incrementally construct the BWT and FM-index of large string sets such as those produced by Next Generation Sequencing. The algorithm is designed for massive parallelism and can effectively exploit the combination of low capacity high bandwidth memory and slower external system memory typical of GPU accelerated systems. Particularly, for a string set of n characters from an alphabet with σsymbols, it uses a constant amount of high-bandwidth memory and at most 3n log(σ) bits of system memory. Given that deep memory hierarchies are becoming a pervasive trait of high performance computing architectures, we believe this to be a relevant feature. The implementation can handle reads of arbitrary length and is up to 2 and respectively 6.5 times faster than state-of-the-art for short and long genomic reads