The Exterior Graded Swiss-Cheese Operad ${\mathrm{\Lambda }}_V^{S^2}$ (with an appendix by Ana Lorena Gherman and Mihai D. Staic)

In this paper we present a construction which is a generalization of the exterior algebra of a vector space $V$. We show how this fits in the language of operads, discuss some properties, and give explicit computations for the case $dim(V)=2$.