I don't believe it matters what we think repentance is. But what it actually is.
*G3340
μετανοέω
metanoeō
met-an-o-eh'-o
From G3326 and G3539; to think differently or afterwards, that is, reconsider (morally to feel compunction): - repent.
G3326
μετά
meta
met-ah'
A primary preposition (often used adverbially); properly denoting accompaniment; “amid” (local or causal); modified variously according to the case (genitive case association, or accusative case succession) with which it is joined; occupying an intermediate position between G575 or G1537 and G1519 or G4314; less intimate than G1722, and less close than G4862): - after (-ward),X that he again, against, among, X and, + follow, hence, hereafter, in, of, (up-) on, + our, X and setting, since, (un-) to, + together, when, with (+ -out). Often used in composition, in substantially the same relations of participation or proximity, and transfer or sequence.
G3539
νοιέω
noieō
noy-eh'-o
From G3563; to exercise the mind (observe), that is, (figuratively) to comprehend, heed: - consider, perceive, think, understand.
G3563
νοῦς
nous
nooce
Probably from the base of G1097; the intellect, that is, mind (divine or human; in thought, feeling, or will); by implication meaning: - mind, understanding. Compare G5590.[/color]
So I think from reading these few Greek references we can come to the conclusion that to Repent means to think differently about something (notably the sin in our lives, and our own self will); which will consequently lead to us turning away from it.