This type of question pops up occasionally and up to a point it really baffles me, but at the same time, in the age of information, it is a valid question. I am not surprised that even though it has been proven obsolete, many people might think Albanians are from the Caucasus.
Preface - What is ethnicity?
An ethnic group or ethnicity is a category of people who identify with each other based on similarities, such as common ancestral, language, social, cultural or national experiences. Unlike other social groups (wealth, age, hobbies), ethnicity is often an inherited status based on the society in which one lives. - as seen on Ethnic group.
What we know?
The Albanians first appear in the historical record in Byzantine sources of the 11th century. At this point, they were already fully Christianized. Very little evidence of pre-Christian Albanian culture survives, although Albanian mythology and folklore are of Paleo-Balkanic origin and almost all of their elements are pagan, in particular showing Greek influence.
The Albanian language forms a separate branch of Indo-European, first attested in the 15th century, and is considered to have evolved from one of the Paleo-Balkanic languages of antiquity.
Studies in genetic anthropology show that the Albanians share similar ancestry to many other Europeans, and especially other peoples of the Balkans.
Albanian are also one of Europe's populations that has most common ancestors within their own ethnic group even though they share ancestors with other ethnic groups. - as seen on Origin of the Albanians.
Conclusion
So, yeah, Albanians are ethnically Albanians. And judging on how fast common ancestral, language, social, cultural factors have changed with Albanians, we can say that they have been so for a long, long, time.