R$\mathbb {R}$‐motivic stable stems

We compute some R$\mathbb {R}$‐motivic stable homotopy groups. For s−w⩽11$s - w \leqslant 11$, we describe the motivic stable homotopy groups πs,w$\pi _{s,w}$ of a completion of the R$\mathbb {R}$‐motivic sphere spectrum. We apply the ρ$\rho$‐Bockstein spectral sequence to obtain R$\mathbb {R}$‐motivic Ext$\operatorname{Ext}$ groups from the C$\mathbb {C}$‐motivic Ext$\operatorname{Ext}$ groups, which are well understood in a large range. These Ext$\operatorname{Ext}$ groups are the input to the R$\mathbb {R}$‐motivic Adams spectral sequence. We fully analyze the Adams differentials in a range, and we also analyze hidden extensions by ρ$\rho$, 2, and η$\eta$. As a consequence of our computations, we recover Mahowald invariants of many low‐dimensional classical stable homotopy elements.