Blackboard bold greek letters

The OP cites this question, Who can write a package for the new mathbb font as in the picture and compatible with Computer Modern font?, as a desired endpoint, in which it appears that an outline font is offered.

For work in pdflatex, and adapting my answer here: Outline text using TrueType fonts, you can set color of border, fill and line-thickness metric, and use pdf specials to accomplish the outline.

\documentclass{article}
\usepackage{xcolor}
\input pdf-trans
\newbox\qbox
\def\usecolor#1{\csname\string\color@#1\endcsname\space}
\newcommand\bordercolor[1]{\colsplit{1}{#1}}
\newcommand\fillcolor[1]{\colsplit{0}{#1}}
\newcommand\outline[1]{\leavevmode%
  \def\maltext{\mydelim #1\mydelim}%
  \setbox\qbox=\hbox{\maltext}%
  \boxgs{Q q 2 Tr \bbthickness\space w \fillcol\space \bordercol\space}{}%
  \copy\qbox%
}
\newcommand\mathbb[1]{\def\mydelim{$}\outline{#1}}
\newcommand\textbb[1]{\def\mydelim{}\outline{#1}}
\newcommand\colsplit[2]{\colorlet{tmpcolor}{#2}\edef\tmp{\usecolor{tmpcolor}}%
  \def\tmpB{}\expandafter\colsplithelp\tmp\relax%
  \ifnum0=#1\relax\edef\fillcol{\tmpB}\else\edef\bordercol{\tmpC}\fi}
\def\colsplithelp#1#2 #3\relax{%
  \edef\tmpB{\tmpB#1#2 }%
  \ifnum `#1>`9\relax\def\tmpC{#3}\else\colsplithelp#3\relax\fi
}
\bordercolor{black}
\fillcolor{white}
\newcommand\bbthickness{.15}
\begin{document}
$y=\mathbb{\beta}+\textbb{R}$
\end{document}

Blackboard bold letters used to be faked by (over)printing the base letter with a slight displacement, like this old FAQ on (La)TeX:

 A set of LaTeX macros for a ``lazy person's'' blackboard bold are:
       \newcommand{\R}{{\sf R\hspace*{-0.9ex}\rule{0.15ex}%
       {1.5ex}\hspace*{0.9ex}}}
       \newcommand{\N}{{\sf N\hspace*{-1.0ex}\rule{0.15ex}%
       {1.3ex}\hspace*{1.0ex}}}
       \newcommand{\Q}{{\sf Q\hspace*{-1.1ex}\rule{0.15ex}%
       {1.5ex}\hspace*{1.1ex}}}
       \newcommand{\C}{{\sf C\hspace*{-0.9ex}\rule{0.15ex}%
       {1.3ex}\hspace*{0.9ex}}}

You'd have to tweak your own fakes.

A very simple solution:

\documentclass[a4paper,12pt]{article}
\usepackage[outline]{contour}
\newcommand*{\fancy}[1]{{\color{white}\contour{black}{#1}}}
\begin{document}
\fancy{$\Gamma\Delta$}$\Gamma$$\Delta$\fancy{$\Xi\Theta\Delta$}
\end{document}