Was Priya helping Sator?

Question

After watching Tenet I'm somewhat confused about Priya's role in the story.

From the beginning, it seems like she works for Tenet and her goal aligns with the rest of the organization.

But when the Protagonist travels back to Oslo with Neil and Kat and then meets Priya again, based on their conversation it seems like it was her goal all along to have Sator acquire the complete algorithm (I watched the dubbed version, so I can't speak of the authenticity of their dialogue).

So was Priya helping Sator? Why did she want Sator to have the complete algorithm?

Answer 1

Priya was not helping Sator.

The reason she wanted The Protagonist to get the algorithm and lose it is because Sator has all the other 8 parts. No one is able to locate these other 8 parts. The team gains access to only one of the parts at the Kiev Opera. They realize that only when Sator gets the final part, will he expose the location of the algorithm as he needs to trigger it to end the world.

When Sator gets his hands on the algorithm he does exactly this. The battle of Stalsk-12 is Sator planning the triggering of the algorithm.

What Priya is keen on doing is finding and killing Kat. The Protagonist doesn't want this. He knows leaving Priya alive will only result in her trying time and over to kill Kat. Though he doesn't want to he chooses Kat's life over Priya's.

Answer 2

MovieMe's answer is correct, but there is another big aspect to it as well. Basically the entirety of Tenet's plan is about making Sator believe that he's won. The idea is that if Sator didn't get the last piece of the algorithm then he'd continue trying to get it, and since he has basically infinite resources being sent to him from the future it's likely that he'd succeed.

Sator's convoluted plan is to put all the pieces together and then bury them under a nuclear bomb. His death will trigger a message to the future, recording the location of the buried algorithm, so that the people in the future can dig it up and activate it, thus ending the world for everyone in the present. In his last moments Sator believes he's been successful, but in fact he hasn't, because the algorithm is pulled out from under the bomb at the last moment. As a result, Sator dies without being able to change the outcome, and his plan can't continue.

So the Tenet plan is to let Sator almost succeed but then thwart him in the last moments of the final battle. This might seem like a risky plan, but it's not, because it's a temporal pincer movement. The whole thing is set up by a future version of the protagonist, who has lived through it once and knows exactly how it will play out. Priya is acting, under his orders, to make sure things happen they way they always did: the protagonist must fail to capture the last component of the algorithm, and the soldiers must fail to defuse the bomb, in order for the splinter unit to be successful in capturing the algorithm in the end.