ground of Arduino and ground of power source

Thanks for the comments from both.

So the jump wire from uno output is actually to ground the metal part of female BNC connector (in the attached photo 2 yellow cable). Sorry maybe my drawing in that part isn't correct.
This is how I wire power source (white as 0v, red as -28V) to 7805, 7805 ouput pin to uno input pin, uno output pin to BNC (orange) and the ground from uno (blue).
So do you think grounding BNC in this setting will be an issue??

The access to part for me currently is radio shack. Am not very familiar with isolator, will that make the voltage conversion less cumbersome??