Strange Behavior Upon Introducing New Hen

My boyfriend, Tyler, and I just added a Plymouth Rock pullet to our pre-existing flock of four. Naturally they jumped on her and antagonized her a bit, but a few days in, she seems to be holding her own. I am sure in a week it will be like nothing ever happened...

Anyway, just today we were observing the birds as usual when we noticed our Red Star carrying around one of the Plymouth's tail feathers in her mouth like a trophy. She was holding it high, and when the others saw, they ran for it like they wanted it too (I swear, I couldn't make this up). So Red Star runs from the others and takes the feather to a distant corner where they normally dirt-bathe. She proceeds to vigorously clean the feather, tossing up dirt all over the place, for about 10 minutes (a long time for a chicken activity). We then witnessed her carrying it around the yard again.

We have owned chickens for over a year now, so while there are many things that don't surprise us, I certainly don't claim to have seen it all. What on EARTH could she have been doing? Ironically she used to be at the bottom of the pecking order, so I have definitely seen her make extra effort to show the little Plymouth who's boss. But this was almost ritualistic--so far outside of any realm of chicken intelligence that I ever would have imagined. Has anyone seen this before?