For the enactment of inter-organizational business processes, blockchain can guarantee the enforcement of process models and the integrity of execution traces. However, existing solutions come with downsides regarding throughput scalability, latency, and suboptimal tradeoffs between confidentiality and transparency. To address these issues, we propose to change the foundation of blockchain-based business process execution: from on-chain smart contracts to state channels, an overlay network on top of a blockchain. State channels allow conducting most transactions off-chain while mostly retaining the core security properties offered by blockchain. Our proposal, process channels, is a model-driven approach to enacting processes on state channels, with the aim to retain the desired blockchain properties while reducing the on-chain footprint as much as possible. We here focus on the principled approach of state channels as a platform, to enable manifold future optimizations in various directions, like latency and confidentiality. We implement our approach prototypical and evaluate it both qualitatively (w.r.t. assumptions and guarantees) and quantitatively (w.r.t. correctness and gas cost). In short, while the initial deployment effort is higher with state channels, it typically pays off after a few process instances; and as long as the new assumptions hold, so do the guarantees.