 Óláfr 's marriage to the daughter of one of Alexander the King of Scots ' most trusted northern lords , and the lord 's assistance rendered to Óláfr and Páll , may suggest that Óláfr had gained Alexander 's approval against Rögnvaldr . In the summer following the defeat of Guðrøðr on Skye , the chronicle states that Óláfr took hostages from the Hebridean portion of the kingdom and , with a fleet of 32 ships , landed on Mann and confronted Rögnvaldr directly . It was then agreed that the kingdom would be split between the two — with Rögnvaldr keeping Mann itself along with the title of king , and Óláfr retaining the Hebridean portions . In the 1220s Alexander began to extend Scottish royal authority into what is today the western coast Scotland , making several expeditions into Argyll . A this time Ruaidrí may have been forced from his lands in Kintyre and replaced by Alexander , installing Domnall mac Ragnaill , a more palatable member of Clann Somairle , in his place . Óláfr 's control of Lewis and Skye , bordering the domains of Clann Somairle , may have made him appear as a potentially valuable ally to Alexander 's eyes , who wished to rein in the more dangerous members of Clann Somairle . 
