Ἀυτόλυκος was Odysseus’ maternal grandfather. According to some traditions (Apollodorus 1.112, Pausanias 8.4.6, Ovid Metamorphoses 13.146), Autolykos is the son of Hermes (thus making Odysseus Hermes’ great-grandson). In Odyssey 19.395–396, Autolykos is said be a favorite of Hermes and “preeminent among men in thieving and perjury” (ἀνθρώπους ἐκέκαστο / κλεπτοσύνῃ θ’ ὅρκῳ τε), a gift given by Hermes himself. Odysseus is in turn a favorite of Autolykos (see Odyssey 19.393ff.). The relationship with Autolykos is one of many links that Odysseus has to the god Hermes, with whom he shares the epithet πολύτροπος (“of many turns,” Odyssey 1.1; Homeric Hymn to Hermes 13). Hermes is the god described in the Homeric Hymn to Hermes 13–18 as “crafty of counsel, a robber, a driver of cattle, a leader of dreams, a spy at night, a thief at the gates … Born at dawn, at mid-day he played the lyre, in the evening he stole the cattle of far-shooting Apollo.” Athena’s intelligence is central to the attested ambush episodes in Homeric epic (see on 10.275), but Hermes’ thieving and crafty ways play a vital role as well. (See also on 10.41 above for the use of the formula νύκτα δι᾽ ὀρφναίην in the Homeric Hymn to Hermes 578.) Here Autolykos is said to have stolen the boar’s tusk helmet that Odysseus wears from a house that is pukinos. The house, in other words, is carefully and solidly built. Its many beams and planks are closely joined one upon the other, much as the boar’s tusks are made to fit seamlessly around the helmet. The word pukinos unites the mētis associated with Odysseus, his maternal grandfather, and Hermes with the cunning required to break into a well-built house and the craft required to construct such a helmet. The invocation of the history of Autolykos’ cunning thievery here thus places Odysseus’ own cunning in a continuum that stretches back through several generations, much as Diomedes’ role in the night raid of Iliad is placed in the context of his father Tydeus’ ambush history in 10.285–286. See 10.5–9 for more on the meanings of pukinos, especially as it relates to ambush.
For a similar “lineage” of an object of prestige, see the history of Agamemnon’s scepter at Iliad 2.101–108. The fact that the object was originally stolen does not seem to disqualify it from becoming a valued guest-gift.