Connect Arduino to 12V Battery

I am starting a project and I would like to connect Arduino to a circuit linked to a 12V battery in order to switch it On/Off by remote. I would like to know if it is possible to link Arduino to such a powerful battery and if there is a way to send input from long distances.( i thought about 3G module or iridium)

The product specs recommend that an Uno should be powered by 7-12v and can be powered by up to 20v so there would be no problem connecting to a 12v battery.

...R

The addition of "3G and iridium" suggest high current draw.

Yes, most Arduinos can run on 12volt.
No, most Arduinos can't provide much power to sensors at that supply voltage.
An Uno for example will get into trouble (overheating regulator) when it has to supply more than ~100mA to sensors.

Power of the battery is irrelevant. A load (Arduino) only takes what it needs.

Be specific, and list actual items used. And a connection diagram.
Leo..