You can adopt an air of nonchalance, a fake British accent, or even a stray dog. When you adopt something, you consciously select it and accept it as your own.
The word adopt has many different shades of meaning, but most relate to the notion of taking something on and treating it as if it’s your own. You’re probably familiar with what happens if you adopt a child: you take on parental responsibilities and accept the child as if it’s your own. You can adopt other things — such as a plan, a method, or a point of view — in a similar way. For example, when you adopt a particular attitude — such as a respectful attitude — you select that as a way to present yourself and behave as if it is natural.