Automaticaly switch on/off an (APC) UPS
Why do you need to turn off the actual ups? How about controlling the devices connected to it instead?  Could you power off torrent server PC (assuming it's a PC) and configure the bios to turn it back on at a specified time? (Many BIOS'es have this feature built in.)  or Wake-On-LAN can do something similar, and there are ways of routing WOL packets over the internet (a more advanced option). 

alternately,you could toggle an electrical outlet using a Solid State Relay (readily available on eBay) rated for the voltage and load being attached, and control it with an Arduino or other microcontroller.  I bet you could get accurate enough timing with Arduino that you wouldn't need a realtime clock module (RTC), but those are also available and can communicate with Arduino using SPI or I2C interface. With a SSR, you could leave the UPS on, and switch the power coming out of the UPS.  To power up your server, many BIOS'es have the option to 'Power On' when power is restored after power loss. NOTE: be sure to properly shut down your server before killing the power to it, by initiating the proper shutdown command, to avoid corrupting your data.

I built an extension cord for 120VAC with a SSR tucked away inside the plug housing for about $25. It's easy to control with an Arduino or anything that can supply a 5VDC signal.

Hope this helps!