The other way around.
The ground can be located at the Arduino but the amp's negative input should be grounded through the capacitor, not directly connected to ground.
And... With a 100W amplifier, I'd recommend a volume-control pot, especially during the development/experimentation phase. Plus, you might want to lower the power supply voltage to the amp and/or put a resistor in series with the speaker to keep the power down to reasonable levels. You don't really want to get a 100W "pop" when you connect something or when you power-on, etc.