The Norse sagas credit Thorfinn the Great with rampaging through Scotland and being proclaimed king. How is he connected with the story?
In the late 10th and early 11th centuries, the northernmost province of Scotland--Caithness--was held by the Norse, along with the Orkney Islands just north across the Pentland Strait. They were the domain of Sigurd the Stout, a jarl (earl) of the Norse king. When Sigurd already had two grown sons, he divorced their mother to marry the daughter of Malcolm King of Scots--an alliance quite possibly part of a peace treaty. For years, it was assumed this Malcolm was Malcolm II, the ruler of Alba; however, one scholar has recently proposed that it might have been Malcolm of Moray, cousin to Macbeth. As noted elsewhere, rulers of Moray as well as Alba were referred to as "King of Scots" in the Irish annals.
Neither one would be surprising. Malcolm II may have used a marriage alliance to gain nominal claim to the province of Caithness, previously a Scottish holding. In that case, Thorfinn was his grandson and had the proper lineage to claim the high kingship. And if we also accept that Macbeth's mother was another daughter of Malcolm II, then Thorfinn and Macbeth were first cousins. If, however, Thofinn's mother was the daughter of Malcolm of Moray, it would have been one in a long line of marriages between the northern Scots and the Norse on their border. It might also explain the relative peace between Caithness and Moray after the battle of Skitten Myre.
When Thorfinn was five years old, his father was killed in the battle of Clontarf. Sigurd's earldom was then divided between his three sons, with Caithness going to Thorfinn. Under Celtic law, the boy was not eligible to rule, but under Norse law, he could and did, aided by Thorkel Amundson, known as Thorkel Fosterer. Together they won the balance of the earldom from Thorfinn's half-brothers, and the young man became a powerful force in the north.
In the Norse sagas, two notable conflicts with the Scots are attributed to Thorfinn: the aforementioned rampage across Scotland to claim the kingship, and a sea battle in the Moray Firth against someone called only Karl Hundeson. Scholars continue to argue over who Karl Hundeson really was: Gillecomgain, whose father was known to the Norse as "the dog earl"? Macbeth? Duncan? What is obvious to one scholar is questionable to another, and we simply do not know.
As for Thorfinn claiming the high kingship, there is no corroborating evidence of that in any of the annals or king lists, which there surely would be if Thorfinn had, indeed, been acknowledged as ruler of Alba. The sagas, on the other hand, were intended to be grandiose, and since they were not written down until 200 years later, and there is certainly room for error in them. But why would they make such a claim?
One writer of fiction has suggested that Thorfinn and Macbeth were the same person. From my research, I cannot agree. Another hypothesis--one that I like--is that Thorfinn and Macbeth were close allies, and after Macbeth defeated Duncan in northern Moray, Thorfinn marched with him to Scone to make his claim and to support him. There is additional evidence to suggest such an alliance, including a later raid by Thorfinn into Northumbria from the west just as Macbeth was attacking from the north, forcing the Northumbrian earl to divide his army.