Similar to the Ibn Ezra's view brought by @JoelK, Rabbi Alexander Hool wrote in an article titled "Who Was The Pharaoh of Yetzias Mitzrayim?", published in Ami's Double Pesach Issue, and which I surmise is a condensed version of his book "Pharaoh: Biblical History, Egypt and the Missing Millennium":
"When Yaakov came back from Charan to live with his father Yitzchak in Chevron, the verse says that there wasn't enough pasture for the flocks of both Yaakov and Esav, so Esav left with his family. Intriguingly, it doesn't divulge where he went, mentioning only later that he went to Har Se'ir. The pasuk also specifies that the chieftains of Odah and Bosmas lived in the land of Edom, but doesn't do so with regard to the chieftains of his third wife, Oholivamah.
From excavations at Avaris, we now know that just around this time there was an influx of Canaanites to the north of Egypt, an area rich in pasture that is close to Chevron. They prospered there for several centuries, turning Avaris into one of the largest cities in the ancient world. Archeologists have also found a sculpture from that period of a red-haired Canaanite wearing a multicolored coat [I think it's this one], reminiscent of the red-haired Esav wearing the coat of many colors that the Midrash says he took from Nimrod.
What seems to have happened is that Esav moved first to Avaris and sometime afterwards left for Se'ir, later to be called Edom, leaving behind the family of Oholivamah. This might have been a tactical move, as Oholivamah was the granddaughter of Se'ir, whose people, the Chori, Esav went on to destroy (Devarim 2:12). Had they gone with Esav, they might have sided with the Chori. What this means is that throughout Bnei Yisrael's sojourn in Egypt they were actually living side-by-side with the descendants of Esav in neighboring Avaris. Indeed, Chazal tell us the people who lived in the same region as Bnei Yisrael were much worse than those in the rest of Egypt. We now know why. They weren't Egyptian but Edomites from Canaan whose behavior was repulsive.
Now let's go back to the Sixth Dynasty Hyksos rulers.
According to the ancient historian Manetho, Teti, the first of the Sixth Dynasty rulers, was not an Egyptian...Why would a Hyksos king set up his capital there [in Avaris]...unless he himself was an Edomite?
This may be what the Torah is alluding to at the end of Parshas Vayishlach. The pasuk lists eight kings that ruled in Edom "before the reign of the king over Bnei Yisrael"...in light of the above, we can now suggest that it might also be alluding to the other kings of Esav, who ruled over Bnei Yisrael in Egypt. Accordingly, Teti would have been the first of the Dynasty of Edomites who ruled over the north of Egypt, and it was he who started the subjugation of Bnei Yisrael..."