Write a program that is valid after circular character shift
Use the right language for the task. In this case, that's Befunge.

This language naturally allows rotations because:


All commands are a single character.
The control wraps around when it reaches the end of the program, starting again from the beginning.


This Befunge program prints the exact same output ("Hello") regardless of how many "circular character shifts" you use:

86*01p75*1-02p447**1-03p439**04p439**05p455**1+06p662**07p75*1-08p645**2-09p69*4+019+p57*029+p59*1-039+p555**1-049+p88*059+p86*01p75*1-02p447**1-03p439**04p439**05p455**1+06p662**07p75*1-08p645**2-09p69*4+019+p57*029+p59*1-039+p555**1-049+p88*059+p645**2-00p645**2-00p


It runs on Befungee. It requires that the board is increased (not the 80 character default). It can be run like this:

python befungee.py -w400 hello.bef


It works by first dynamically generating and storing a program that prints "Hello" and then overwriting the first byte to redirect the control into the newly written program. The program is written twice so that if a byte is not written correctly the first time, it will be corrected the second time.

The idea could be extended to produce any program of arbitrary complexity.