This paper presents a kernel-based adaptive filter that is applied for the digital domain self-interference cancellation (SIC) in a transceiver operating in full-duplex (FD) mode. In FD, the benefit of simultaneous transmission and receiving of signals comes at the price of strong self-interference (SI). In this work, we are primarily interested in suppressing the SI using an adaptive filter namely adaptive projected subgradient method (APSM) in a reproducing kernel Hilbert space (RKHS) of functions. Using the projection concept as a powerful tool, APSM is used to model and consequently remove the SI. A low-complexity and fast-tracking algorithm is provided taking advantage of parallel projections as well as the kernel trick in RKHS. The performance of the proposed method is evaluated on real measurement data. The method illustrates the good performance of the proposed adaptive filter, compared to the known popular benchmarks. They demonstrate that the kernel-based algorithm achieves a favorable level of digital SIC while enabling parallel computation-based implementation within a rich and nonlinear function space, thanks to the employed adaptive filtering method.