@dhark I bought
one of these C13/C14/5-15R power taps to add a powered gadget near my projector without having to run an additional power cable (although I only paid $13 for mine). Maybe if your AVR has the same C14 power input, you could use something similar?
Here's one for $10.
That will, of course, supply constant power. If you prefer your accessory to power off at the same time as your AVR, then consider
a smart power strip. I've got two of these to kill the power to my Roku devices when their attached displays are powered off, and they've performed flawlessly despite their low cost.