The GeForce RTX 4070 WINDFORCE OC 12G (12 GB) with a length of 26.1 cm and 200 W power consumption could physically fit into an HP OMEN 880, provided the case offers sufficient space and the network delivers enough power. However, the available HP specifications for the OMEN 880 models lack concrete information on the maximum supported graphics card length and the power connection (e.g. PCIe power connectors).

Important points on compatibility:
- Physical fit: The card is 26.1 cm long - compare this with the available space in the case (especially with components such as fans or cables already installed).
- Power supply: The card requires 200 W - check whether the OMEN 880 power supply offers sufficient capacity and the required PCIe power connections (e.g. 1× 12VHPWR or adapter).
- BIOS/software: Update the BIOS version of the OMEN 880 to avoid possible compatibility issues with newer GPUs.

Without detailed information on the specific OMEN 880 model (e.g. housing dimensions, power supply unit), compatibility cannot be definitively confirmed. In case of uncertainty, I recommend checking the technical documentation of the PC or contacting HP support.