If I’m living in area A which is NOT on Shabbat time and I cause an Electrical Event ( lights, circuit, router, etc..) to be activate in area B which is IN Shabbat time. Is this consider a violation of Shabbat ? This is apply to two areas : (1) phone – if I call someone (and s/he didn’t pick up the phone) and I cause the phone to ring on Shabbat . (2) Can I go on web sites (like www.a7.org) which I know that the people there are Shabbat observers but by me going on their web site I cause the lights on their router to turn on, the computer to operate, their hard drive to access data etc…
There is no prohibition of "shvitat kelim" and therefore what you describe is permitted (see Shmirat Shabbat 31, 26).