Cobordism is a famous equivalence relation between compact manifolds of the same dimension. It was first introduced by Henri Poincaré, but then very much studied by Lev Pontrjagin and René Thom. Nowadays, the classic results have been generalized and cobordism has become a useful tool in a lot of scientific fields. Nested cobordism extends the notion of cobordism by considering manifolds together with embedded submanifolds, together with embedded submanifolds… and so on. It is then worth to study how the results known for cobordism translate to the nested setting. In particular, I will deal with the so called Pontrjagin construction. At this point you might be wondering what role bananas play in all this… Well, you will see!