"Wannabes" attempting to self-identify with another country? It would help if we knew where you are and which countries they are trying to "be from." I can see, for example, college students adopting affectations from France to better fit in at a cooking class. I can't really see someone saying, "Hey, I'm from [somewhere]! That makes me awesome purely on the basis of being from [somewhere]!"
On the other hand, I have read about U.S. tourists claiming to be from Canada to avoid all the anti-American sentiment common overseas, so that might be interesting in this discussion.
In my experience, students take on affectations because they are insecure and want to be accepted. In high-school, difference is either good or bad: good if it is seen as "cool," bad if it is seen as easily-mocked. If they are pretending to be from another country, it is likely symptomatic of problems at home and a feeling of alienation; if they are "other," or foreign, they have a shield against local unhappiness.
I think we need to remember that students in high school go through a massive period of flux where they are uncertain of who they are. It is perfectly normal therefore for such students to play with different roles and identities as part of working out who they want themselves to be. This may be what the behaviour you allude to refers to.
There is a concept in sociolinguistics called accommodation theory and it is tightly connected to the concepts of prestige and negative prestige. Studies have shown, for example those in Denmark, that children, young people, and teens may be motivated to accommodate negative prestige (or positive prestige) aspects of sociolinguistic behavior based upon television programing they watch (believe it or not!) in a sociolinguistic dynamic.
[Sociolinguistic dynamic is how social behavior and interaction is expressed by yet influenced by language in an influence that goes both directions, from speaker to society and/or from society to speaker.]
What the first paragraph means is that the sociolinguistic dynamic witnessed in television shows can dominated sociolinguistic reality in daily experience and that this dominating influence can be favorable as prestige, as in upholding national linguistic standards such as preserving diversity of dialects (as is desired in Denmark), or it can be unfavorable as negative prestige, as in spreading the East London dialect to areas far removed from East London (as is occurring in England).
All this is to suggest that it is possible this/these group/s at school are experiencing the effects of interpersonal accommodation theory [they are influenced either favorably or unfavorably by a sociolinguistic dynamic they are experiencing, such as one or some television show or shows] as studies in Denmark and England have shown to be possible.
It does appear that these young people have identity issues, as indeed many teenagers do. Finding one's true self is a tough battle for some, and the search for an identity with which one is comfortable can be a challenging path.
Have you considered trying to talk to one or more members of the group? You may find that their image is a defence mechanism, and as there are a number of them, they may be simply trying to cultivate a group they are comfortable with. Many teenage groups can be described as 'wannabees'. Not all of the jocks are real athletes, lots of the goths do not drink blood or spend their lives in misery. These are roles adopted to identify with a discrete group.
I used to teach in a rural area where most of the students came from very poor families. The last thing that any of the kids wanted to admit were that they were poor. Many of the kids spent every last cent they had on expensive, trendy clothes to try and fool their classmates. They bragged about non-existent rich relatives and out-of-town girlfriends and boyfriends. The identity issue is always something that most teens are trying to conquer.
Is it possible that they are reflecting/identifying with countries that do figure in their heritage, just not immediately evident or more than one generation removed? Many residents of the United States can claim a number of "home countries" in their ancestry that may not be obvious associations.
Previous posts also make good points about possible explanations. If the students are doing a good job of being authentic in how they are dressing/acting/eating, you might want to take advantage of the opportunity to learn about those countries.
I would have to say that many students, especially younger ones in middle school and early years in high school, are trying to find their own identity. While their identity may not be what they are "impersonating," they may simply be searching for an identity outside of the norm. It is my belief that they are simply in search for a new self.
pohnpei's answer, as usual, is very strong. It would be helpful to know which country they are pretending to be from. Then we would be in a better position to guess at their motives. Is it a wealthy country? An exotic country? A country associated with cultural sophistication? And which country are they in right now? Knowing the answers to some of these questions would help us give you better feedback.
It's hard to know exactly what your situation is, but typically, the teen years are a time to try on various identities. It is a time to try on personalities and identities that are not really who you are. In a sense, it's rebelling against who you have been as a kid and it's also an attempt to figure out who you will be as an adult. I think that's why people pretend to be things they're not in high school -- it's because they're teens and that's what teens do.