If you restrict it to the vaccinated population and the unvaccinated population, then you can consider the vaccinated population fully populated, and the unvaccinated population entirely unvaccinated.

Vaccinated group:

Rt = 6 * ( 1 - (1 * .8)) = 1.2

Unvaccinated group:

Rt = 6 * ( 1 - (0 * .8)) = 6

The question of "how much less" is hard to parse, but the point is that even among the vaccinated group (in this scenario), the virus is still spreading and growing exponentially.

I suppose if Rt was clearly below 1 for the vaccinated group, that might mean something, but if the groups intermingle, that advantage would be lost pretty quickly.

I think you are still missing my point. You are using a circular definition of R0. Where did you get that number 6? Is that for a fully unvaccinated population? Are partially vaccinated population? If so, what percentage? Your calculation makes absolutely no sense, it's circular. You can't calculate R0 using R0.

No, R0=6 is a given. I'm not calculating R0. R0 for Delta is estimated between 5 and 9.5. I picked 6, just for illustration. Given a starting R0 and a vaccination rate and a vaccine effectiveness, that is how you can calculate effective Rt. There's nothing circular about that.

There's no such thing as "R0 within a vaccinated community" - R0 is the starting reproductive number. Effective reproductive number - given various mitigation measures like vaccination, masks, natural immunity, etc - is Rt.

You can try the calculations using any other starting R0, from 5 to 9.5 if you stay consistent with estimates of Delta transmissibility.

The point is that it's possible that a group of vaccinated people would never have an Rt below 1 from vaccination alone, simply because of the limited vaccine effectiveness against transmission.

If one population spreads a disease more than another, it makes absolutely no sense that R0 is a constant across all populations, by definition. Perhaps you should look up the meaning of R0.