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Making general particle transport simulation for high-energy physics (HEP) single-instruction-multiple-thread (SIMT) friendly, to take advantage of accelerator hardware, is an important alternative for boosting the throughput of simulation applications. To date, this challenge is not yet resolved, due to difficulties in mapping the complexity of Geant4 components and workflow to the massive parallelism features exposed by graphics processing units (GPU). The AdePT project is one of the R\&D initiatives tackling this limitation and exploring GPUs as potential accelerators for offloading some part of the CPU simulation workload. Our main target is to implement a complete electromagnetic shower demonstrator working on the GPU. The project is the first to create a full prototype of a realistic electron, positron, and gamma electromagnetic shower simulation on GPU, implemented as either a standalone application or as an extension of the standard Geant4 CPU workflow. Our prototype currently provides a platform to explore many optimisations and different approaches. We present the most recent results and initial conclusions of our work, using both a standalone GPU performance analysis and a first implementation of a hybrid workflow based on Geant4 on the CPU and AdePT on the GPU.