Connecting a Google Stadia Controller with Bluetooth to the OUYA is not possible.
The Stadia controller uses Bluetooth Low Energy (BLE).
According to ifixit, the OUYA’s bluetooth chipset is based on a “Broadcom BCM4330” chip, which supports Bluetooth 4.0. Its data sheet says:
The BBC supports Bluetooth 4.0 features with the following benefits:
- Dual mode Bluetooth Low Energy (BT and BLE operation).
But when putting the controller into pairing mode, the OUYA does not see it.
The reason is that the Android 4.1 used by the OUYA does not support BLE - only Android 4.3+ does:
Bluetooth Low Energy (BLE), available in Android 4.3 and later, creates short connections between devices to transfer bursts of data.
So even USB bluetooth dongles with BLE will not help.