Tsezar is one of the most important people in the book in terms of Shukhov. In a way, Tsezar is sort of the idiot rich guy that Shukhov is cleverly conning. Thanks to Tsezar's ineptitude, or badness, at caring for himself, Shukhov is able to repeatedly help Tsezar out and get rewards in return.
Tsezar is actually a lot like Captain Buynovsky. Both are young, both think they are hot stuff, both are having trouble adapting to camp life, and both have a lot of pride. But pride definitely doesn't amount to much in the camp, and Tsezar, for all his academic smarts and good connections, is pretty powerless at the end of the day. A well-educated director, he's forced to rely on an ex-peasant/carpenter for help at the end of the day. And Tsezar seems to realize the importance of Shukhov by the day's end. Check out these two contrasting interactions between Tsezar and Shukhov.
"Ahem!" Shukhov cleared this throat. He felt awkward, interrupting this educated conversation, but he couldn't just go on standing there.
Tsezar turned around and held his hand out for the bowl, without even looking at Shukhov - the gruel might have traveled from the air unaided - then went back to his argument. (497-498)
Here Tsezar kind of lives up to his name, which is a Russian version of "Caesar," like the dictator not the salad. He's very pompous, or full of it here, acting like some sort of aristocrat and treating Shukhov like a servant, or a waiter. But here's a scene from the end of the novel, where we see a big difference in Tsezar's behavior.
Shukhov saw that Tsezar was in a panic – but he should have thought of it sooner. He was shoving the fatback and the sausage under his shirt – if nothing else, he might be able to take them out to roll call and save them.
Shukhov took pity on him and told him how it was done. (133-134)
There's a definite shift in the balance of power here and the confident and at times arrogant Tsezar is reduced to a panicky doofus, while Shukhov is the knowledgeable guy in charge. For all his education, Tsezar definitely lacks street smarts. His character serves as another example of someone from a relatively higher class having trouble adapting to camp life. The former film director spends half his time discussing movies rather than focusing on his survival.
Tsezar also helps to demonstrate the kind of symbiotic relationships that form in the camp between unlikely people. Shukhov and Tsezar both rely on one another in a lot of ways and end up helping one another out throughout the day.