## 1 Introduction  
In the field of cognitive sciences, the ability that enables a person to feel their own body parts, initiate and control their own actions, and perceive mental states as their own is known as the sense of embodiment (SoE) [1; 2; 3; 4; 5]. SoE has been identified as a necessary component for achieving health outcomes and behaviors [6; 7] and may be compromised under clinical conditions [8; 9; 10; 11]. SoE is not limited to our own physical body but can also be induced through the perception and illusory control of a virtual or robotic body or body parts [12; 13; 14; 15; 16; 17; 18]. While there are various definitions of SoE concerning external bodies, in this study, we adopt the definition provided by [PERSON] and colleagues [3]. According to these authors, SoE is a sense that arises when the properties of an external body are processed as if they were the properties of one's own biological body [3]. Furthermore, it has been demonstrated that some aspects of SoE can be achieved simply by being in control of objects that bear no human resemblance [17; 19; 20]. Measuring SoE has posed a challenge for empirical research, and several attempts have been made to find standardized psychometric measures [5; 21; 22]. In addition to subjective measures, there have been endeavors to measure embodiment through electrophysiological recordings [23; 24], skin conductance responses (SCRs) [25; 26; 27], or body temperature measurements [28; 29]. SoE can be broken down into three underlying components: the sense of self-location (SoL), the sense of ownership (SoO), and the sense of agency (SoA) [3]. While some studies do not differentiate between these components or employ different terminology, an analysis of the subjective questions used allows associating each of them with one of these three categories. According to [PERSON] and colleagues (et al., 2012), the subjective experience of recognizing oneself as the agent of certain behaviors is described as SoA, the feeling that a body (or its parts) belongs to the person is referred to as SoO, and the experience of being situated in the space where one's body is located is denoted as SoL. SoO can be considered in a broader sense, where it includes the feeling of mineness not only of the body (body ownership) and its parts (limb-ownership) but also of feelings and thoughts (see [PERSON] et al., 2018, for a review) [30]. Meanwhile, the same authors highlight that SoA allows not only the distinguishing between self- and other-generated actions but also the intention to generate motor activity (i.e., motor imagery). Although there have been multiple studies on the neurophysiological basis of embodiment, its evaluation is usually complemented by the use of questionnaires [31; 32; 33; 34; 35]. There are several studies demonstrating that the illusory experience of the body increases with the use of a brain-machine interface (BMI) or brain-computer interface (BCI) [14; 15; 36; 37; 38]. However, to be able to understand how BMIs influence embodiment, it is necessary to define and classify BMIs. In general terms, BMI technology enables the use of brain activity (or a proxy) decoded in real time to control an external device [39; 40]. The terms BMI and BCI are generally considered synonymous terms [41]. Here, we will adopt the BMI to refer to both BMI and BCI. There are different types of BMIs and some of them can be categorized as active BMIs or as reactive BMIs [39]. The active BMI is a system that uses neural activity resulting from voluntary activity, as occurs during motor imagery (i.e., thinking about walking). Motor imagery-based BMIs (MI-BMIs) are the most used type of BMI. On the other hand, a reactive BMI is a system that uses brain signals resulting from a reaction to an external stimulus. A very common example of this is the steady-state visually evoked potentials (SSVEPs), where changes in brain activity are evoked in the visual cortex through a visual stimulus flickering at a specific frequency [39].