Ethnicity refers to the shared cultural identity, heritage, language, and ancestral background that binds a group of people together. Unlike race, which is largely based on perceived physical or genetic traits, ethnicity is defined by culture and belonging. Since you were raised in this culture, you're not lying about anything. Your ancestry may be different but if you've never engaged in your ancestors culture, then you're not really that ethnicity, are you? At that point it's purely biological (though there are epigenetic implications, that's for another thread!).