A Software Product Line (SPL) is a family of similar programs (called variants) generated from a common artifact base. Variability in an SPL can be documented in terms of abstract description of functionalities (called features): a feature model (FM) identifies each variant by a set of features (called a product). Delta-orientation is a flexible approach to implement SPLs. An SPL Signature (SPLS) is a variability-aware Application Programming Interface (API), i.e., an SPL where each variant is the API of a program. In this paper we introduce and formalize, by abstracting from SPL implementation approaches, the notion of slice of an SPLS K for a set of features F (i.e., an SPLS obtained from by K by hiding the features that are not in F). Moreover, we formulate the challenge of defining an efficient algorithm that, given a delta-oriented SPLS K and a set of features F, returns a delta-oriented SPLS that is an slice of K for F. Thus paving the way for further research on devising such an algorithm. The proposed notions are formalized for SPLs of programs written in an imperative version of Featherweight Java.